diff --git a/doc/rst/source/cookbook/options.rst b/doc/rst/source/cookbook/options.rst
index 8c962595e42..c49a5f38813 100644
--- a/doc/rst/source/cookbook/options.rst
+++ b/doc/rst/source/cookbook/options.rst
@@ -287,23 +287,27 @@ tick, and gridline intervals, axes labels, and annotation units.
 
 The Frame settings are specified by
 
--  **-B**\ [*axes*][**+b**][**+g**\ *fill*][**+i**\ [*val*]][**+n**][**+o**\ *lon/lat*][**+t**\ *title*]
+-  **-B**\ [*axes*][**+b**][**+g**\ *fill*][**+i**\ [*val*]][**+n**][**+o**\ *lon/lat*][**+t**\ *title*][**+w**\ [*pen*]][**+x**\ *fill*][**+y**\ *fill*][**+z**\ *fill*]
 
 Here, the optional *axes* dictates which of the axes should be drawn
-and possibly annotated.  By default, all 4 map boundaries (or plot axes)
+and possibly annotated.  By default, all four map boundaries (or plot axes)
 are plotted (denoted **W**, **E**, **S**, **N**). To change this selection,
 append the codes for those you want (e.g., **WSn**). In this example,
 the lower case **n** denotes to draw the axis and (major and minor) tick
 marks on the "northern" (top) edge of the plot. The upper case **WS** will
 annotate the "western" and "southern" axes with numerals and plot the
 any axis labels in addition to draw axis/tick-marks.  For 3-D plots you can
-also specify **Z** or **z**.  By default a single vertical axes will then be
+also specify **Z** or **z**.  To *just* draw an axis without annotation and
+ticks you can use the **l**\ (eft), **r**\ (ight), **b**\ (ottom), **t**\ (op)
+and (for 3-D) **u**\ (p) codes. By default, a single vertical axes will then be
 plotted at the most suitable map corner.  You can override this by appending
 any combination of corner ids **1234**, where **1** represents the lower left
-corner and the order goes counter-clockwise.  Append **+b** to draw the outline
-of the 3-D box defined by **-R**; this modifier is also needed to display
-gridlines in the x–z, y–z planes.  You may paint the
-map canvas by appending the **+g**\ *fill* modifier [Default is no fill].
+corner and the order goes counter-clockwise.  Use **+w** to draw the outlines of
+the x-z and y-z planes [no outlines] and optionally append the *pen* to use
+[:term:`MAP_GRID_PEN_PRIMARY`]. Alternatively, append **+b** to also draw the front lines
+of the 3-D cube defined by **-R**.  You can paint the interior of the canvas with
+**+g**\ *fill* (this also sets fill for the two back-walls in 3-D).
+Use **+x**, **+y**, and **+z** to control the painting of planes *yz*, *xz* and *xy*, respectively [Default is no fill].
 Use **+i** to annotate an internal meridian or parallel when the axis that normally
 would be drawn and annotated does not exist (e.g., azimuthal map with 360-degree range
 has no latitude axis, and a global Hammer map has no longitude axis);
diff --git a/doc/rst/source/explain_-B_full.rst_ b/doc/rst/source/explain_-B_full.rst_
index 568f3cfd4e0..3fbc88b3986 100644
--- a/doc/rst/source/explain_-B_full.rst_
+++ b/doc/rst/source/explain_-B_full.rst_
@@ -3,22 +3,24 @@
 **-B**\ [**p**\|\ **s**]\ *parameters*
     Set map Frame and Axes parameters. The Frame parameters are specified by
 
-    **-B**\ [*axes*][**+b**][**+g**\ *fill*][**+i**\ [*val*]][**+n**][**+o**\ *lon/lat*][**+t**\ *title*]
+    **-B**\ [*axes*][**+b**][**+g**\ *fill*][**+i**\ [*val*]][**+n**][**+o**\ *lon/lat*][**+t**\ *title*][**+w**\ [*pen*]][**+x**\ *fill*][**+y**\ *fill*][**+z**\ *fill*]
 
-    where *axes* selects which axes to plot. By default, all 4 map boundaries
+    where *axes* selects which axes to plot. By default, all four map boundaries
     (or plot axes) are plotted (named **W**, **E**, **S**, **N**). To customize,
     append the codes for those you want (e.g., **WSn**). Upper case means plot
     and annotate while lower case just plots and ticks the specified axes.
     To *just* draw an axis without annotation and ticks you can use the **l**\ (eft),
-    **r**\ (ight), **b**\ (ottom), **t**\ (opt) and (for 3-D) **u**\ (p) codes. If a 3-D basemap
-    is selected with **-p** and **-Jz**, append **Z**, **z**, or **u** to control the
-    appearance of the vertical axis. By default a single vertical axes will be
-    plotted at the most suitable map corner. Override the default by appending
+    **r**\ (ight), **b**\ (ottom), **t**\ (op) and (for 3-D) **u**\ (p) codes.
+    If a 3-D basemap is selected with **-p** and **-Jz**, append **Z**, **z**, or
+    **u** to control the appearance of the vertical axis. By default a single vertical
+    axes will be plotted at the most suitable map corner. Override the default by appending
     any combination of corner ids **1234**, where **1** represents the lower left
-    corner and the order goes counter-clockwise. Append **+b** to draw the outline of the 3-D
-    cube defined by **-R**; this modifier is also needed to display gridlines in
-    the x-z, y-z planes. Note that for 3-D views the title, if given, will be
-    suppressed. You can paint the interior of the canvas with **+g**\ *fill*.
+    corner and the order goes counter-clockwise.  Use **+w** to draw the outlines of
+    the x-z and y-z planes [no outline] and optionally append the *pen* to use
+    [:term:`MAP_GRID_PEN_PRIMARY`]. Alternatively, append **+b** to also draw the front lines
+    of the 3-D cube defined by **-R**. You can paint the interior of the canvas with
+    **+g**\ *fill* (this also sets fill for the two back-walls in 3-D).
+    Use **+x**, **+y**, and **+z** to control the painting of planes *yz*, *xz* and *xy*, respectively [Default is no fill]. 
     Use **+i** to annotate an internal meridian or parallel when the axis that normally
     would be drawn and annotated does not exist (e.g., azimuthal map with 360-degree range
     has no latitude axis, and a global Hammer map has no longitude axis); optionally append the parallel or meridian [0].
diff --git a/src/gmt_init.c b/src/gmt_init.c
index 43069fa6ddc..dfe81ac3e4a 100644
--- a/src/gmt_init.c
+++ b/src/gmt_init.c
@@ -2473,14 +2473,14 @@ GMT_LOCAL bool gmtinit_true_false_or_error (char *value, bool *answer) {
 }
 
 /*! . */
-GMT_LOCAL int gmtinit_decode4_wesnz (struct GMT_CTRL *GMT, const char *in, unsigned int side[], bool *draw_box, int part) {
+GMT_LOCAL int gmtinit_decode4_wesnz (struct GMT_CTRL *GMT, const char *in, unsigned int side[], unsigned int *draw_box, int part) {
 	/* Scans the WESNZwesnz+ flags at the end of string "in" and sets the side/drawbox parameters
 	 * and returns the length of the remaining string.  Assumes any +g<fill> has been removed from in.
 	 */
 
 	int i, k, orig_i;
-	unsigned int side_orig[5];
-	bool go = true, orig_draw_box = *draw_box;
+	unsigned int side_orig[5], orig_draw_box = *draw_box;
+	bool go = true;
 
 	GMT->current.map.frame.set_frame[part]++;
 	if (GMT->current.map.frame.set_frame[GMT_PRIMARY] > 1 || GMT->current.map.frame.set_frame[GMT_SECONDARY] > 1) {
@@ -2496,7 +2496,7 @@ GMT_LOCAL int gmtinit_decode4_wesnz (struct GMT_CTRL *GMT, const char *in, unsig
 	for (k = 0; go && i >= 0 && strchr ("WESNZwesnz+", in[i]); i--) {
 		if (k == 0 && part == 0) {	/* Wipe out default values when the first flag is found */
 			for (k = 0; k < 5; k++) side[k] = 0;
-			*draw_box = false;
+			*draw_box = GMT_3D_NONE;
 		}
 		if (in[i] == 's') {	/* Since s can mean both "draw south axis" and "seconds", check further */
 			if (side[S_SIDE]) go = false;	/* If S was set already then s probably means seconds */
@@ -2518,7 +2518,7 @@ GMT_LOCAL int gmtinit_decode4_wesnz (struct GMT_CTRL *GMT, const char *in, unsig
 			case 'n': side[N_SIDE] |= GMT_AXIS_BARB; break;
 			case 'z': side[Z_SIDE] |= GMT_AXIS_BARB; break;
 			/* Draw 3-D box */
-			case '+': *draw_box = true; break;
+			case '+': *draw_box = GMT_3D_BOX; break;
 		}
 	}
 	if (i >= 0 && in[i] == ',') i--;	/* Special case for -BCcustomfile,WESNwesn to avoid the filename being parsed for WESN */
@@ -3749,7 +3749,7 @@ GMT_LOCAL int gmtinit_parse4_B_option (struct GMT_CTRL *GMT, char *in) {
 	gmtinit_handle_dosfile (GMT, in, 0);	/* Temporarily replace DOS files like X:/ with X;/ to avoid colon trouble */
 #endif
 
-	for (i = (int)strlen(in) - 1, ignore = false; !GMT->current.map.frame.paint && !error && i >= 0; i--) {	/** Look for +g<fill */
+	for (i = (int)strlen(in) - 1, ignore = false; !GMT->current.map.frame.paint[GMT_Z] && !error && i >= 0; i--) {	/** Look for +g<fill */
 		if (in[i] == ':') ignore = !ignore;
 		if (ignore) continue;	/* Not look inside text items */
 		if (in[i] == '+' && in[i+1] == 'o') {	/* Found +o<plon>/<plat> */
@@ -3775,9 +3775,9 @@ GMT_LOCAL int gmtinit_parse4_B_option (struct GMT_CTRL *GMT, char *in) {
 #ifdef _WIN32
 			gmtinit_handle_dosfile (GMT, out1, 1);	/* Undo any DOS files like X;/ back to X:/ */
 #endif
-			if (gmt_getfill (GMT, out1, &GMT->current.map.frame.fill)) error++;
+			if (gmt_getfill (GMT, out1, &GMT->current.map.frame.fill[GMT_Z])) error++;
 			if (!error) {
-				GMT->current.map.frame.paint = true;
+				GMT->current.map.frame.paint[GMT_Z] = true;
 				g = i;
 				in[g] = '\0';	/* Chop off +g for now */
 			}
@@ -3948,12 +3948,14 @@ GMT_LOCAL int gmtinit_decode5_wesnz (struct GMT_CTRL *GMT, const char *in, bool
 			/* Draw 3-D box */
 			case '+':
 				if (in[k+1] == 'b')	/* Got +b appended to MAP_FRAME_AXES, possibly */
-					GMT->current.map.frame.draw_box = true;
+					GMT->current.map.frame.draw_box |= GMT_3D_BOX;
+				else if (in[k+1] == 'w')	/* Got +w appended to MAP_FRAME_AXES, possibly */
+					GMT->current.map.frame.draw_box |= GMT_3D_WALL;
 				else if (in[k+1] == 'n')	/* Got +n appended to MAP_FRAME_AXES, means no frame nor annotations desired */
 					GMT->current.map.frame.no_frame = true;
 				else if (gmt_M_compat_check (GMT, 4)) {
 					GMT_Report (GMT->parent, GMT_MSG_COMPAT, "Modifier + in MAP_FRAME_AXES is deprecated; use +b instead.\n");
-					GMT->current.map.frame.draw_box = true;
+					GMT->current.map.frame.draw_box |= GMT_3D_BOX;
 				}
 				else {
 					GMT_Report (GMT->parent, GMT_MSG_ERROR, "Modifier + in MAP_FRAME_AXES not recognized.\n");
@@ -3987,6 +3989,10 @@ bool gmtlib_B_is_frame (struct GMT_CTRL *GMT, char *in) {
 	if (strstr (in, "+n")) return true;	/* Found a +n so likely frame */
 	if (strstr (in, "+o")) return true;	/* Found a +o so likely frame */
 	if (strstr (in, "+t")) return true;	/* Found a +t so likely frame */
+	if (strstr (in, "+w")) return true;	/* Found a +w so likely frame */
+	if (strstr (in, "+x")) return true;	/* Found a +x so likely frame */
+	if (strstr (in, "+y")) return true;	/* Found a +y so likely frame */
+	if (strstr (in, "+z")) return true;	/* Found a +z so likely frame */
 	if (strstr (in, "+a")) return false;	/* Found a +a so likely axis */
 	if (strstr (in, "+f")) return false;	/* Found a +f so likely axis */
 	if (strstr (in, "+l")) return false;	/* Found a +l so likely axis */
@@ -4003,11 +4009,13 @@ bool gmtlib_B_is_frame (struct GMT_CTRL *GMT, char *in) {
 
 /*! . */
 GMT_LOCAL int gmtinit_parse5_B_frame_setting (struct GMT_CTRL *GMT, char *in) {
+	bool did_g = false;
 	unsigned int pos = 0, k, error = 0;
 	char p[GMT_BUFSIZ] = {""}, text[GMT_BUFSIZ] = {""}, *mod = NULL;
 	double pole[2];
+	struct GMT_FILL F;
 
-	/* Parsing of -B<framesettings>: -B[<axes>][+b][+g<fill>][+n][+o<lon>/<lat>][+t<title>] */
+	/* Parsing of -B<framesettings>: -B[<axes>][+b][+g<fill>][+n][+o<lon>/<lat>][+t<title>][+w[<pen>]][+x<fill>][+y<fill>][+z<fill>] */
 
 	/* First determine that the given -B<in> string is indeed the framesetting option.  If not return -1 */
 
@@ -4018,23 +4026,25 @@ GMT_LOCAL int gmtinit_parse5_B_frame_setting (struct GMT_CTRL *GMT, char *in) {
 	/* OK, here we are pretty sure this is a frame -B statement */
 
 	strncpy (text, in, GMT_BUFSIZ-1);
-	gmt_handle5_plussign (GMT, text, "bginot", 0);	/* Temporarily change double plus-signs to double ASCII 1 to avoid +<modifier> angst */
+	gmt_handle5_plussign (GMT, text, "bginotwxyz", 0);	/* Temporarily change double plus-signs to double ASCII 1 to avoid +<modifier> angst */
 	GMT->current.map.frame.header[0] = '\0';
+	gmt_M_memset (GMT->current.map.frame.paint, 3U, bool);
+	GMT->current.map.frame.draw_box = GMT_3D_NONE;
 
 	if ((mod = strchr (text, '+'))) {	/* Find start of modifiers, if any */
 		while ((gmt_strtok (mod, "+", &pos, p))) {	/* Parse any +<modifier> statements */
 			switch (p[0]) {
-				case 'b':	/* Activate 3-D box and x-z, y-z gridlines (if selected) */
-					GMT->current.map.frame.draw_box = true;
+				case 'b':	/* Draw 3-D box */
+					GMT->current.map.frame.draw_box |= (GMT_3D_BOX|GMT_3D_WALL);
 					break;
-				case 'g':	/* Paint the basemap interior */
-					if (p[1] == 0 || gmt_getfill (GMT, &p[1], &GMT->current.map.frame.fill)) {
+				case 'g':	/* Paint the basemap x-y plane and for 3-D back walls */
+					if (p[1] == 0 || gmt_getfill (GMT, &p[1], &F)) {
 						GMT_Report (GMT->parent, GMT_MSG_ERROR, "Bad +g<fill> argument %s\n", &p[1]);
 						error++;
 					}
-					GMT->current.map.frame.paint = true;
+					did_g = true;
 					break;
-				case 'i':	/* Turn on internal annotation for radiual or longitudinal axes when there is no other place to annotate */
+				case 'i':	/* Turn on internal annotation for radial or longitudinal axes when there is no outside place to annotate */
 					GMT->current.map.frame.internal_annot = 1;	/* Longitude/angle */
 					if (GMT->current.proj.projection == GMT_POLAR)	/* Optional argument is an angle, not longitude, so atof will do */
 						GMT->current.map.frame.internal_arg = (p[1]) ? atof (&p[1]) : GMT->common.R.wesn[XLO];
@@ -4082,6 +4092,40 @@ GMT_LOCAL int gmtinit_parse5_B_frame_setting (struct GMT_CTRL *GMT, char *in) {
 						gmtlib_enforce_rgb_triplets (GMT, GMT->current.map.frame.header, GMT_LEN256);	/* If @; is used, make sure the color information passed on to ps_text is in r/b/g format */
 					}
 					break;
+				case 'w':	/* Set back-wall outline and optionally the pen to use */
+					GMT->current.map.frame.draw_box |= GMT_3D_WALL;
+					GMT->current.map.frame.draw_wall = true;	/* We will draw the outline of the walls */
+					if (p[1] && gmt_getpen (GMT, &p[1], &GMT->current.map.frame.pen)) {
+						GMT_Report (GMT->parent, GMT_MSG_ERROR, "Bad +w<pen> argument %s\n", &p[1]);
+						error++;
+					}
+					else if (p[1] == 0)	/* Use grid pen as default */
+						gmt_M_memcpy (&GMT->current.map.frame.pen, &GMT->current.setting.map_grid_pen[GMT_PRIMARY], 1, struct GMT_PEN);
+					break;
+				case 'x':	/* Paint the basemap yz-plane for 3-D plots */
+					if (p[1] == 0 || gmt_getfill (GMT, &p[1], &GMT->current.map.frame.fill[GMT_Y])) {
+						GMT_Report (GMT->parent, GMT_MSG_ERROR, "Bad +x<fill> argument %s (or possibly missing)\n", &p[1]);
+						error++;
+					}
+					GMT->current.map.frame.paint[GMT_Y] = true;
+					GMT->current.map.frame.draw_box |= GMT_3D_WALL;
+					break;
+				case 'y':	/* Paint the basemap xz-plane for 3-D plots */
+					if (p[1] == 0 || gmt_getfill (GMT, &p[1], &GMT->current.map.frame.fill[GMT_X])) {
+						GMT_Report (GMT->parent, GMT_MSG_ERROR, "Bad +y<fill> argument %s (or possibly missing)\n", &p[1]);
+						error++;
+					}
+					GMT->current.map.frame.paint[GMT_X] = true;
+					GMT->current.map.frame.draw_box |= GMT_3D_WALL;
+					break;
+				case 'z':	/* Paint the basemap xy-plane for 3-D plots */
+					if (p[1] && gmt_getfill (GMT, &p[1], &GMT->current.map.frame.fill[GMT_Z])) {
+						GMT_Report (GMT->parent, GMT_MSG_ERROR, "Bad +z<fill> argument %s\n", &p[1]);
+						error++;
+					}
+					GMT->current.map.frame.paint[GMT_Z] = true;
+					GMT->current.map.frame.draw_box |= GMT_3D_WALL;
+					break;
 				default:
 					GMT_Report (GMT->parent, GMT_MSG_ERROR, "Option -B: Unrecognized frame modifier %s\n", p);
 					error++;
@@ -4091,6 +4135,19 @@ GMT_LOCAL int gmtinit_parse5_B_frame_setting (struct GMT_CTRL *GMT, char *in) {
 		*mod = '\0';	/* Separate the modifiers from the frame selectors */
 	}
 
+	if (!GMT->current.map.frame.paint[GMT_X] && did_g) {	/* Let +g set all sides not already set */
+		gmt_M_memcpy (&GMT->current.map.frame.fill[GMT_X], &F, 1U, struct GMT_FILL);
+		GMT->current.map.frame.paint[GMT_X] = true;
+	}
+	if (!GMT->current.map.frame.paint[GMT_Y] && did_g) {	/* Let +g set all sides not already set */
+		gmt_M_memcpy (&GMT->current.map.frame.fill[GMT_Y], &F, 1U, struct GMT_FILL);
+		GMT->current.map.frame.paint[GMT_Y] = true;
+	}
+	if (!GMT->current.map.frame.paint[GMT_Z] && did_g) {	/* Let +g set all sides not already set */
+		gmt_M_memcpy (&GMT->current.map.frame.fill[GMT_Z], &F, 1U, struct GMT_FILL);
+		GMT->current.map.frame.paint[GMT_Z] = true;
+	}
+
 	/* Now parse the frame choices, if any */
 	error += gmtinit_decode5_wesnz (GMT, text, true);
 
@@ -4105,6 +4162,7 @@ void gmt_init_B (struct GMT_CTRL *GMT) {
 		for (k = 0; k < 6; k++) GMT->current.map.frame.axis[no].item[k].parent = no;
 		if (GMT->current.proj.xyz_projection[no] == GMT_TIME) GMT->current.map.frame.axis[no].type = GMT_TIME;
 	}
+	gmt_M_memset (GMT->current.map.frame.paint, 3U, bool);
 	GMT->common.B.string[0][0] = GMT->common.B.string[1][0] = '\0';
 	GMT->current.map.frame.init = true;
 	GMT->current.map.frame.draw = false;
@@ -4115,11 +4173,13 @@ void gmt_init_B (struct GMT_CTRL *GMT) {
 GMT_LOCAL int gmtinit_parse5_B_option (struct GMT_CTRL *GMT, char *in) {
 	/* GMT5 clean version based on new syntax:
 	 * Frame settings:
-	 *	-B[WESNwesnz|Z[1234]][+b][+g<fill>][+o<lon/lat>][+t<title>]
-	 *    		+b enables 3-D box and x-z, y-z gridlines.
-	 *    		+g<fill> as plot interior fill [none].
+	 *	-B[WESNwesnz|Z[1234]][+b][+g<fill>][+o<lon/lat>][+t<title>][+w[<pen>]][+x<fill>][+y<fill>][+z<fill>]
+	 *    		+b draws 3-D box.
+	 *    		+g<fill> as plot interior fill and backwalls (if 3-D) [none].
 	 *    		+t<title> as plot title [none].
+	 *    		+w[<pen>] draws the outline of the xz and yz planes [no outline].
 	 *    		of one or more of w,e,s,n,z then only those axes will be drawn.
+	 *    		+x, +y, +z paints the back walls for yz, xz, xy [with +g fill if not specified].
 	 *		Upper case letters means the chosen axes also will be annotated.
 	 *		Default is determined by MAP_FRAME_AXES setting [WESN].
 	 * Axis settings:
@@ -4162,8 +4222,8 @@ GMT_LOCAL int gmtinit_parse5_B_option (struct GMT_CTRL *GMT, char *in) {
 	if ((error = gmtinit_parse5_B_frame_setting (GMT, in)) >= 0) return (error);	/* Parsed the -B frame settings separately */
 	error = 0;	/* Reset since otherwise it is -1 */
 
-	if (strstr (in, "+b") || strstr (in, "+g") || strstr (in, "+i") || strstr (in, "+n") || strstr (in, "+o") || strstr (in, "+o") || strstr (in, "+t")) {
-		GMT_Report (GMT->parent, GMT_MSG_ERROR, "Option -B: Found frame setting modifiers (+b|g|i|n|o|p) mixed with axes settings!\n");
+	if (strstr (in, "+b") || strstr (in, "+g") || strstr (in, "+i") || strstr (in, "+n") || strstr (in, "+o") || strstr (in, "+o") || strstr (in, "+t") || strstr (in, "+w") || strstr (in, "+x") || strstr (in, "+y") || strstr (in, "+z")) {
+		GMT_Report (GMT->parent, GMT_MSG_ERROR, "Option -B: Found frame setting modifiers (+b|g|i|n|o|p|W) mixed with axes settings!\n");
 		return (GMT_PARSE_ERROR);
 	}
 
@@ -5835,7 +5895,7 @@ void gmt_conf (struct GMT_CTRL *GMT) {
 	/* MAP_FRAME_AXES */
 	strcpy (GMT->current.setting.map_frame_axes, "WESNZ");
 	for (i = 0; i < 5; i++) GMT->current.map.frame.side[i] = 0;	/* Unset default settings */
-	GMT->current.map.frame.draw_box = false;
+	GMT->current.map.frame.draw_box = GMT_3D_NONE;
 	error += gmtinit_decode5_wesnz (GMT, "WESNZ", false);
 	/* MAP_DEFAULT_PEN */
 	error += gmt_getpen (GMT, "default,black", &GMT->current.setting.map_default_pen);
@@ -6513,24 +6573,25 @@ void gmtlib_explain_options (struct GMT_CTRL *GMT, char *options) {
 
 			gmt_message (GMT, "\t-B Specify both (1) basemap frame settings and (2) axes parameters.\n");
 			gmt_message (GMT, "\t   Frame settings are modified via an optional single invocation of\n");
-			gmt_message (GMT, "\t     -B[<axes>][+b][+g<fill>][+i[<val>]][+n][+o<lon>/<lat>][+t<title>]\n");
+			gmt_message (GMT, "\t     -B[<axes>][+b][+g<fill>][+i[<val>]][+n][+o<lon>/<lat>][+t<title>][+w[<pen>]][+x<fill>][+y<fill>][+z<fill>]\n");
 			gmt_message (GMT, "\t   Axes parameters are specified via one or more invocations of\n");
 			gmt_message (GMT, "\t     -B[p|s][x|y|z]<info>\n\n");
 			gmt_message (GMT, "\t   1. Frame settings control which axes to plot, frame fill, title, and type of gridlines:\n");
 			gmt_message (GMT, "\t     <axes> is a combination of W,E,S,N,Z and plots those axes only [Default is WESNZ (all)].\n");
 			gmt_message (GMT, "\t     Use lower case w,e,s,n,z just to draw and tick (but not annotate) those axes,\n");
 			gmt_message (GMT, "\t     and use l,r,b,t,u just to draw (but not annotate and tick) those axes.\n");
-			gmt_message (GMT, "\t     For 3-D plots the Z|z[<corners>][+b] controls the vertical axis.  The <corners> specifies\n");
-			gmt_message (GMT, "\t     at which corner(s) to erect the axis via a combination of 1,2,3,4; 1 means lower left corner,\n");
-			gmt_message (GMT, "\t     2 is lower right, etc., in a counter-clockwise order. [Default automatically selects one axis].\n");
-			gmt_message (GMT, "\t     The optional +b will erect a 3-D frame box to outline the 3-D domain [no frame box]. The +b\n");
-			gmt_message (GMT, "\t     is also required for x-z or y-z gridlines to be plotted (if such gridlines are selected below).\n");
 			gmt_message (GMT, "\t     Append +g<fill> to paint the inside of the map region before further plotting [no fill].\n");
 			gmt_message (GMT, "\t     Append +i<val> to annotate along parallel or meridian <val> [0] when no such axes can be plotted.\n");
 			gmt_message (GMT, "\t     Append +n to have no frame and annotations whatsoever [Default is controlled by WESNZ/wesnz].\n");
 			gmt_message (GMT, "\t     Append +o<plon>/<plat> to draw oblique gridlines about this pole [regular gridlines].\n");
 			gmt_message (GMT, "\t     Note: the +o modifier is ignored unless gridlines are specified via the axes parameters (below).\n");
 			gmt_message (GMT, "\t     Append +t<title> to place a title over the map frame [no title].\n");
+			gmt_message (GMT, "\t     For 3-D plots the Z|z[<corners>] controls the vertical axis.  The <corners> specifies\n");
+			gmt_message (GMT, "\t     at which corner(s) to erect the z-axis via a combination of 1,2,3,4; 1 means lower left corner,\n");
+			gmt_message (GMT, "\t     2 is lower right, etc., in a counter-clockwise order [Default automatically selects one axis].\n");
+			gmt_message (GMT, "\t     The +w draws the outline of the xz and yz planes [no outlines].\n");
+			gmt_message (GMT, "\t     The +x|y|z[<fill>] paint the yz, xz, xy planes [no fill]. The +g<fill> sets all three planes.\n");
+			gmt_message (GMT, "\t     In addition, +b will erect a 3-D frame box to outline the 3-D domain [no frame box].\n");
 			gmt_message (GMT, "\t   2. Axes settings control the annotation, tick, and grid intervals and labels.\n");
 			gmt_message (GMT, "\t     The full axes specification is\n");
 			gmt_message (GMT, "\t       -B[p|s][x|y|z]<intervals>[+a<angle>|n|p][+f][+l|L<label>][+p<prefix>][+s|S<secondary_label>][+u<unit>]\n");
@@ -6545,8 +6606,7 @@ void gmtlib_explain_options (struct GMT_CTRL *GMT, char *options) {
 			gmt_message (GMT, "\t     To prepend a prefix to each annotation (e.g., $ 10, $ 20 ...), add +p<prefix>.\n");
 			gmt_message (GMT, "\t     To append a unit to each annotation (e.g., 5 km, 10 km ...), add +u<unit>.\n");
 			gmt_message (GMT, "\t     Cartesian x-axis takes optional +a<angle> for slanted or +an for orthogonal annotations [+ap].\n");
-			gmt_message (GMT, "\t     Cartesian y-axis takes optional +ap for parallel annotations [+an].\n");
-			gmt_message (GMT, "\t     Cartesian z-axis takes optional +an for parallel annotations [+an].\n");
+			gmt_message (GMT, "\t     Cartesian y- and z-axes take optional +ap for parallel annotations [+an].\n");
 			gmt_message (GMT, "\t     Geographic axes take optional +f for \"fancy\" annotations with W|E|S|N suffices.\n");
 			gmt_message (GMT, "\t     To label an axis, add +l<label>.  Use +L to enforce horizontal labels for y-axes.\n");
 			gmt_message (GMT, "\t     For another axis label on the opposite axis, use +s|S as well.\n");
@@ -7658,8 +7718,8 @@ void gmt_syntax (struct GMT_CTRL *GMT, char option) {
 	switch (option) {
 
 		case 'B':	/* Tickmark option */
-			gmt_message (GMT, "\t-B[p|s][x|y|z]<intervals>[+a<angle>|n|p][+l|L<label>][+p<prefix>][+u<unit>] -B[<axes>][+b][+g<fill>][+o<lon>/<lat>][+t<title>] OR\n");
-			gmt_message (GMT, "\t-B[p|s][x|y|z][a|f|g]<tick>[m][l|p] -B[p|s][x|y|z][+l<label>][+p<prefix>][+u<unit>] -B[<axes>][+b][+g<fill>][+o<lon>/<lat>][+t<title>]\n");
+			gmt_message (GMT, "\t-B[p|s][x|y|z]<intervals>[+a<angle>|n|p][+l|L<label>][+p<prefix>][+u<unit>] -B[<axes>][+b][+g<fill>][+o<lon>/<lat>][+t<title>][+w[<pen>]][+x<fill>][+y<fill>][+z<fill>] OR\n");
+			gmt_message (GMT, "\t-B[p|s][x|y|z][a|f|g]<tick>[m][l|p] -B[p|s][x|y|z][+l<label>][+p<prefix>][+u<unit>] -B[<axes>][+b][+g<fill>][+o<lon>/<lat>][+t<title>][+w[<pen>]][+x<fill>][+y<fill>][+z<fill>]\n");
 			break;
 
 		case 'J':	/* Map projection option */
@@ -9728,7 +9788,7 @@ unsigned int gmtlib_setparameter (struct GMT_CTRL *GMT, const char *keyword, cha
 		case GMTCASE_MAP_FRAME_AXES:
 			strncpy (GMT->current.setting.map_frame_axes, value, 5U);
 			for (i = 0; i < 5; i++) GMT->current.map.frame.side[i] = 0;	/* Unset default settings */
-			GMT->current.map.frame.draw_box = false;
+			GMT->current.map.frame.draw_box = GMT_3D_NONE;
 			error += (bool)gmtinit_decode5_wesnz (GMT, value, false);
 			break;
 
@@ -12635,11 +12695,11 @@ GMT_LOCAL struct GMT_CTRL *gmtinit_begin_module_sub (struct GMTAPI_CTRL *API, co
 	GMT->common.p.active = GMT->common.s.active = GMT->common.t.active = GMT->common.colon.active = false;
 	gmt_M_memset (GMT->common.b.ncol, 2, int);
 
-	/* Initialize bg fill to white although we don't use it until GMT->current.map.frame.paint = true;
+	/* Initialize bg fill to white although we don't use it until GMT->current.map.frame.paint[GMT_Z] = true;
 	   But needed when using images with an transparency layer.
 	*/
 
-	GMT->current.map.frame.fill.rgb[0] = GMT->current.map.frame.fill.rgb[1] = GMT->current.map.frame.fill.rgb[2] = 1.0;
+	GMT->current.map.frame.fill[GMT_Z].rgb[0] = GMT->current.map.frame.fill[GMT_Z].rgb[1] = GMT->current.map.frame.fill[GMT_Z].rgb[2] = 1.0;
 
 	*Ccopy = Csave; /* Pass back out for safe-keeping by the module until gmt_end_module is called */
 
@@ -14303,8 +14363,8 @@ void gmt_end_module (struct GMT_CTRL *GMT, struct GMT_CTRL *Ccopy) {
 	gmtinit_free_user_media (GMT);	/* Free user-specified media formats */
 
 	/* Reset frame fill painting */
-	Ccopy->current.map.frame.paint = GMT->current.map.frame.paint;
-	gmt_M_memcpy (Ccopy->current.map.frame.fill.rgb, GMT->current.map.frame.fill.rgb, 3, double);
+	Ccopy->current.map.frame.paint[GMT_Z] = GMT->current.map.frame.paint[GMT_Z];
+	gmt_M_memcpy (Ccopy->current.map.frame.fill[GMT_Z].rgb, GMT->current.map.frame.fill[GMT_Z].rgb, 3, double);
 
 	/* GMT_IO */
 
diff --git a/src/gmt_map.c b/src/gmt_map.c
index 858aa48ae17..f1554f5c81f 100644
--- a/src/gmt_map.c
+++ b/src/gmt_map.c
@@ -6584,7 +6584,7 @@ void gmt_auto_frame_interval (struct GMT_CTRL *GMT, unsigned int axis, unsigned
 	double Hmaj[4] = {2.0, 3.0, 6.0, 12.0}, Hsub[4] = {1.0, 1.0, 3.0, 3.0};
 	double Omaj[4] = {3.0, 6.0}, Osub[4] = {1.0, 3.0};
 	double Dmaj[4] = {2.0, 3.0, 7.0, 14.0}, Dsub[4] = {1.0, 1.0, 1.0, 7.0};
-	double d, f, p, *maj = defmaj, *sub = defsub;
+	double d, f, p, sxy = 1.0, sz = 1.0, *maj = defmaj, *sub = defsub;
 	struct GMT_PLOT_AXIS *A = &GMT->current.map.frame.axis[axis];
 	struct GMT_PLOT_AXIS_ITEM *T;
 
@@ -6595,21 +6595,24 @@ void gmt_auto_frame_interval (struct GMT_CTRL *GMT, unsigned int axis, unsigned
 		!(A->item[item+2].active && A->item[item+2].interval == 0.0) &&
 		!(A->item[item+4].active && A->item[item+4].interval == 0.0)) return;
 
+	if (GMT->current.proj.three_D) {	/* Make an approximate adjustment to the "sizes" given a perspective view */
+		sxy = 1.0 - cosd (GMT->current.proj.z_project.view_elevation);
+		sz  = 1.0 - fabs (sind (GMT->current.proj.z_project.view_elevation));
+	}
 	/* f = frame width/height (inch); d = domain width/height (world coordinates) */
 	if (axis == GMT_X) {
-		f = fabs (GMT->current.proj.rect[XHI] - GMT->current.proj.rect[XLO]);
+		f = sxy * fabs (GMT->current.proj.rect[XHI] - GMT->current.proj.rect[XLO]);
 		d = fabs (GMT->common.R.wesn[XHI] - GMT->common.R.wesn[XLO]);
 	}
 	else if (axis == GMT_Y) {
-		f = fabs (GMT->current.proj.rect[YHI] - GMT->current.proj.rect[YLO]);
+		f = sxy * fabs (GMT->current.proj.rect[YHI] - GMT->current.proj.rect[YLO]);
 		d = fabs (GMT->common.R.wesn[YHI] - GMT->common.R.wesn[YLO]);
 	}
 	else {
-		f = fabs (GMT->current.proj.zmax - GMT->current.proj.zmin);
+		f = sz * fabs (GMT->current.proj.zmax - GMT->current.proj.zmin);
 		d = fabs (GMT->common.R.wesn[ZHI] - GMT->common.R.wesn[ZLO]);
 	}
 	f *= GMT->session.u2u[GMT_INCH][GMT_PT];	/* Change to points */
-
 	/* First guess of interval */
 	d *= MAX (0.05, MIN (5.0 * GMT->current.setting.font_annot[item].size / f, 0.20));
 
@@ -6678,7 +6681,8 @@ void gmt_auto_frame_interval (struct GMT_CTRL *GMT, unsigned int axis, unsigned
 	/* Finally set grid interval (if annotation set as well, use major, otherwise minor interval) */
 	T = &A->item[item+4];
 	if (T->active && T->interval == 0.0) {
-		T->interval = set_a ? d : f, T->generated = true;
+		T->interval = set_a ? d : f, T->generated = true; /* Commented out because f is too fine for gridline spacing, even if no annotations */
+		// T->interval = d, T->generated = true;
 		snprintf (tmp, GMT_LEN16, "g%g", T->interval); strcat (string, tmp);
 		if (is_time) T->unit = unit, strcat (string, sunit);
 	}
diff --git a/src/gmt_parse.c b/src/gmt_parse.c
index 815cf048f87..20107a2f5ec 100644
--- a/src/gmt_parse.c
+++ b/src/gmt_parse.c
@@ -86,7 +86,7 @@ GMT_LOCAL int gmtparse_B_arg_inspector (struct GMT_CTRL *GMT, char *in) {
 	int gmt4 = 0, gmt5 = 0, n_digits = 0, n_colons = 0, n_slashes = 0, colon_text = 0, wesn_at_end = 0;
 	bool ignore = false;	/* true if inside a colon-separated string under GMT4 style assumption */
 	bool ignore5 = false;	/* true if label, title, prefix, suffix */
-	bool custom = false;	/* True if -B[p|s][x|y|z]c<filename> was given; then we relax checing for .c (old second) */
+	bool custom = false;	/* True if -B[p|s][x|y|z]c<filename> was given; then we relax checking for .c (old second) */
 	char mod = 0;
 
 	if (!in || in[0] == 0) return (9);	/* Just a safety precaution, 9 means "either" syntax but it is an empty string */
@@ -124,10 +124,12 @@ GMT_LOCAL int gmtparse_B_arg_inspector (struct GMT_CTRL *GMT, char *in) {
 		if (ignore) continue;	/* Don't look inside a title or label */
 		switch (in[k]) {
 			case '/': if (mod == 0) n_slashes++; break;	/* Only GMT4 uses slashes */
-			case '+':	/* Plus, might be GMT5 modifier switch */
+			case '+':	/* Plus, might be a GMT5 modifier switch */
 				if      (k < last && in[k+1] == 'u') {mod = 'u'; ignore5 = true;  gmt5++;}	/* unit (suffix) settings */
 				else if (k < last && in[k+1] == 'b') {mod = 'b'; ignore5 = false; gmt5++;}	/* 3-D box settings */
 				else if (k < last && in[k+1] == 'g') {mod = 'g'; ignore5 = false; gmt5++;}	/* fill settings */
+				else if (k < last && in[k+1] == 'i') {mod = 'i'; ignore5 = false; gmt5++;}	/* internal annotation settings */
+				else if (k < last && in[k+1] == 'n') {mod = 'n'; ignore5 = true;  gmt5++;}	/* Turn off frames and annotations */
 				else if (k < last && in[k+1] == 'o') {mod = 'o'; ignore5 = false; gmt5++;}	/* oblique pole settings */
 				else if (k < last && in[k+1] == 'p') {mod = 'p'; ignore5 = true;  gmt5++;}	/* prefix settings */
 				else if (k < last && in[k+1] == 'l') {mod = 'l'; ignore5 = true;  gmt5++;}	/* Label */
@@ -135,7 +137,10 @@ GMT_LOCAL int gmtparse_B_arg_inspector (struct GMT_CTRL *GMT, char *in) {
 				else if (k < last && in[k+1] == 's') {mod = 's'; ignore5 = true;  gmt5++;}	/* Secondary label */
 				else if (k < last && in[k+1] == 'S') {mod = 'S'; ignore5 = true;  gmt5++;}	/* Forced horizontal Secondary lLabel */
 				else if (k < last && in[k+1] == 't') {mod = 't'; ignore5 = true;  gmt5++;}	/* title */
-				else if (k < last && in[k+1] == 'n') {mod = 'n'; ignore5 = true;  gmt5++;}	/* Turn off frames and annotations */
+				else if (k < last && in[k+1] == 'w') {mod = 'w'; ignore5 = false; gmt5++;}	/* Pen for walls */
+				else if (k < last && in[k+1] == 'x') {mod = 'x'; ignore5 = false; gmt5++;}	/* Paint for yz plane */
+				else if (k < last && in[k+1] == 'y') {mod = 'y'; ignore5 = false; gmt5++;}	/* Paint for xz plane */
+				else if (k < last && in[k+1] == 'z') {mod = 'z'; ignore5 = false; gmt5++;}	/* Paint for xy plane */
 				else if (k && (in[k-1] == 'Z' || in[k-1] == 'z')) {ignore5 = false; gmt4++;}	/* Z-axis with 3-D box */
 				break;
 			case 'c':	/* If following a number this is unit c for seconds in GMT4 */
diff --git a/src/gmt_plot.c b/src/gmt_plot.c
index 75a30a85327..38c8c19d8f8 100644
--- a/src/gmt_plot.c
+++ b/src/gmt_plot.c
@@ -1556,13 +1556,20 @@ GMT_LOCAL void gmtplot_map_symbol_ns (struct GMT_CTRL *GMT, struct PSL_CTRL *PSL
 	if (nc) gmt_M_free (GMT, xings);
 }
 
-GMT_LOCAL void gmtplot_z_gridlines (struct GMT_CTRL *GMT, struct PSL_CTRL *PSL, double zmin, double zmax, int plane) {
-	unsigned int k, i, nz, item[2] = {GMT_GRID_UPPER, GMT_GRID_LOWER};
-	double dz, zz, min, max, *z = NULL;
+GMT_LOCAL void gmtplot_z_gridlines (struct GMT_CTRL *GMT, struct PSL_CTRL *PSL, double zmin, double zmax, int plane, unsigned int mode3d, int quadrant) {
+	unsigned int k, i, nz, n, item[2] = {GMT_GRID_UPPER, GMT_GRID_LOWER};
+	int qplane = 1 - plane;
+	double dz, zz, dd, min, max, z0, z1, xx, dummy, value, *z = NULL, *d = NULL;
 	char *plane_name[2] = {"y-z", "x-z"};
 
-	min = (plane == GMT_Y) ? GMT->current.proj.rect[XLO] : GMT->current.proj.rect[YLO];
-	max = (plane == GMT_Y) ? GMT->current.proj.rect[XHI] : GMT->current.proj.rect[YHI];
+	if (qplane == GMT_X) {
+		value = (quadrant == 4) ? GMT->common.R.wesn[YHI] : GMT->common.R.wesn[YLO];
+		min = GMT->current.proj.rect[XLO];	max = GMT->current.proj.rect[XHI];
+	}
+	else {
+		value = (quadrant == 3) ? GMT->common.R.wesn[XHI] : GMT->common.R.wesn[XLO];
+		min = GMT->current.proj.rect[YLO];	max = GMT->current.proj.rect[YHI];
+	}
 
 	for (k = 0; k < 2; k++) {
 		if (fabs (GMT->current.setting.map_grid_cross_size[k]) > 0.0) continue;
@@ -1581,10 +1588,30 @@ GMT_LOCAL void gmtplot_z_gridlines (struct GMT_CTRL *GMT, struct PSL_CTRL *PSL,
 			zz = gmt_z_to_zz (GMT, z[i]);
 			PSL_plotsegment (PSL, min, zz, max, zz);
 		}
+		z0 = gmt_z_to_zz (GMT, z[0]);
+		z1 = gmt_z_to_zz (GMT, z[nz-1]);
+
+		dd = gmtlib_get_map_interval (GMT, &GMT->current.map.frame.axis[qplane].item[item[k]]);
+		if (!GMT->current.map.frame.axis[qplane].item[item[k]].active || fabs(dd) == 0.0) continue;
+		n = gmtlib_coordinate_array (GMT, GMT->common.R.wesn[2*qplane], GMT->common.R.wesn[2*qplane+1], &GMT->current.map.frame.axis[qplane].item[item[k]], &d, NULL);
+		for (i = 0; i < n; i++) {	/* Here z acts as y and x|y acts as x */
+			/* Draw one horizontal line */
+			if (qplane == GMT_X)	/* The "x" are projection x or longitude */
+				gmt_geo_to_xy (GMT, d[i], value, &xx, &dummy);
+			else	/* The "x" are projection y or latitude */
+				gmt_geo_to_xy (GMT, value, d[i], &dummy, &xx);
+
+			PSL_plotsegment (PSL, xx, z0, xx, z1);
+		}
+		gmt_M_free (GMT, d);
 
 		PSL_setdash (PSL, NULL, 0);
-		gmt_M_free (GMT, z);
 	}
+	if (!GMT->current.map.frame.draw_wall && z && (mode3d & GMT_3D_BOX) == 0) {
+		PSL_plotsegment (PSL, min, z0, min, z1);
+		PSL_plotsegment (PSL, max, z0, max, z1);
+	}
+	gmt_M_free (GMT, z);
 }
 
 GMT_LOCAL int gmtplot_save_current_gridlines (struct GMT_CTRL *GMT) {
@@ -2625,12 +2652,42 @@ GMT_LOCAL bool gmtplot_is_fancy_boundary (struct GMT_CTRL *GMT) {
 	}
 }
 
-GMT_LOCAL void gmtplot_vertical_wall (struct GMT_CTRL *GMT, struct PSL_CTRL *PSL, int quadrant, double *nesw, bool back) {
-	int plane = (quadrant + 1) % 2;
+GMT_LOCAL void gmtplot_vertical_wall (struct GMT_CTRL *GMT, struct PSL_CTRL *PSL, int quadrant, double *nesw, bool back, unsigned int mode3d) {
+	/* Draws the two vertical walls in the back of the 3-D plot */
+	int plane = (quadrant + 1) % 2;	/* Black magic that gives us GMT_X (for yz plane) or GMT_Y (for xz plane) */
+	double xx[4], yy[4];
+	gmt_plane_perspective (GMT, plane, nesw[quadrant % 4]);
+	/* Assign the coordinates of the four corners of the wall (hence assumed to be rectangular) */
+	xx[0] = xx[1] = nesw[(quadrant+1)%4];	xx[2] = xx[3] = nesw[(quadrant+3)%4];
+	yy[0] = yy[3] = GMT->current.proj.zmin;	yy[1] = yy[2] = GMT->current.proj.zmax;
+	if (mode3d & GMT_3D_WALL && back) {	/* Called for one of the back walls and we wish to draw it */
+		int wplane = 1 - plane;	/* Get integer for the correct plain side */
+		if (GMT->current.map.frame.paint[wplane]) {	/* First paint the back wall, with no outline drawn */
+			PSL_setfill (PSL, GMT->current.map.frame.fill[wplane].rgb, 0);
+			PSL_plotbox (PSL, nesw[(quadrant+1)%4], GMT->current.proj.zmin, nesw[(quadrant+3)%4], GMT->current.proj.zmax);
+		}
+		if (back)	/* Gridlines was requested, so draw those now */
+			gmtplot_z_gridlines (GMT, PSL, GMT->common.R.wesn[ZLO], GMT->common.R.wesn[ZHI], plane, mode3d, quadrant);
+
+		if (GMT->current.map.frame.draw_wall) {	/* We wanted the outline of the back-wall drawn, do now to overwrite any perimeter gridlines */
+			gmt_setpen (GMT, &GMT->current.map.frame.pen);
+			PSL_plotline (PSL, xx, yy, 4, PSL_MOVE|PSL_STROKE);
+		}
+	}
+	else if (back)	/* Get here if no back-walls were filled our outlined */
+		gmtplot_z_gridlines (GMT, PSL, GMT->common.R.wesn[ZLO], GMT->common.R.wesn[ZHI], plane, mode3d, quadrant);
+}
+
+GMT_LOCAL void gmtplot_cube_box (struct GMT_CTRL *GMT, struct PSL_CTRL *PSL, int quadrant, double *nesw) {
+	/* Draws the 3-D cube lines */
+	int plane = (quadrant + 1) % 2;	/* Black magic that gives us GMT_X (for yz plane) or GMT_Y (for xz plane) */
+	double xx[4], yy[4];
 	gmt_plane_perspective (GMT, plane, nesw[quadrant % 4]);
-	PSL_plotbox (PSL, nesw[(quadrant+1)%4], GMT->current.proj.zmin, nesw[(quadrant+3)%4], GMT->current.proj.zmax);
-	if (back)
-		gmtplot_z_gridlines (GMT, PSL, GMT->common.R.wesn[ZLO], GMT->common.R.wesn[ZHI], plane);
+	/* Assign the coordinates of the four corners of the wall (hence assumed to be rectangular) */
+	xx[0] = xx[1] = nesw[(quadrant+1)%4];	xx[2] = xx[3] = nesw[(quadrant+3)%4];
+	yy[0] = yy[3] = GMT->current.proj.zmin;	yy[1] = yy[2] = GMT->current.proj.zmax;
+	gmt_setpen (GMT, &GMT->current.map.frame.pen);
+	PSL_plotline (PSL, xx, yy, 4, PSL_MOVE|PSL_STROKE);
 }
 
 GMT_LOCAL void gmtplot_timestamp (struct GMT_CTRL *GMT, struct PSL_CTRL *PSL, double x, double y, unsigned int justify, char *U_label) {
@@ -5466,7 +5523,7 @@ void gmt_map_basemap (struct GMT_CTRL *GMT) {
 
 	PSL_setdash (PSL, NULL, 0);	/* To ensure no dashed pens are set prior */
 
-	gmt_vertical_axis (GMT, GMT->current.plot.mode_3D);
+	if (GMT->current.proj.three_D && GMT->current.map.frame.drawz) GMT->current.map.frame.plotted_header = true;	/* Just so it is not plotted by gmtplot_map_boundary first */
 
 	if (GMT->current.proj.got_azimuths) gmt_M_uint_swap (GMT->current.map.frame.side[E_SIDE], GMT->current.map.frame.side[W_SIDE]);	/* Temporary swap to trick justify machinery */
 
@@ -5491,6 +5548,10 @@ void gmt_map_basemap (struct GMT_CTRL *GMT) {
 
 	PSL_setdash (PSL, NULL, 0);
 
+	if (GMT->current.proj.three_D && GMT->current.map.frame.drawz) GMT->current.map.frame.plotted_header = false;	/* Now we can plot the title [if selected via -B+t] */
+
+	gmt_vertical_axis (GMT, GMT->current.plot.mode_3D);
+
 	PSL_comment (PSL, "End of basemap\n");
 
 	for (side = 0; side < 4; side++) {	/* Reset annotation crowdedness arrays */
@@ -5504,6 +5565,19 @@ void gmt_map_basemap (struct GMT_CTRL *GMT) {
 	PSL_setcolor (PSL, GMT->current.setting.map_default_pen.rgb, PSL_IS_STROKE);
 }
 
+GMT_LOCAL bool gmtplot_z_axis_side (struct GMT_CTRL *GMT, unsigned int axis, unsigned int quadrant) {
+	bool below;
+	axis++;	/* 1-4 */
+	switch (axis) {
+		case 1: below = (quadrant == 2);	break;
+		case 2: below = (quadrant != 3);	break;
+		case 3: below = (quadrant != 2);	break;
+		case 4: below = (quadrant == 3);	break;
+		default: below = true;	/* Just to avoid Coverity issues */
+	}
+	return below;
+}
+
 void gmt_vertical_axis (struct GMT_CTRL *GMT, unsigned int mode) {
 	/* Mode means: 1 = background walls and title, 2 = foreground walls and axis, 3 = all */
 	unsigned int fore, back, old_plane, form;
@@ -5513,6 +5587,11 @@ void gmt_vertical_axis (struct GMT_CTRL *GMT, unsigned int mode) {
 	if (!GMT->current.proj.three_D) return;
 	if (!GMT->current.map.frame.drawz) return;
 
+	if (GMT->current.map.frame.axis[GMT_Z].item[GMT_GRID_UPPER].active || GMT->current.map.frame.axis[GMT_Z].item[GMT_GRID_LOWER].active) {
+		GMT->current.map.frame.draw_box |= GMT_3D_WALL;
+		GMT->current.map.frame.draw_wall = true;
+	}
+
 	nesw[0] = GMT->current.proj.rect[YHI], nesw[1] = GMT->current.proj.rect[XHI], nesw[2] = GMT->current.proj.rect[YLO], nesw[3] = GMT->current.proj.rect[XLO];
 
 	fore = mode & 2, back = mode & 1;
@@ -5527,12 +5606,18 @@ void gmt_vertical_axis (struct GMT_CTRL *GMT, unsigned int mode) {
 		PSL_setfill (PSL, GMT->session.no_rgb, 1);
 		gmt_setpen (GMT, &GMT->current.setting.map_grid_pen[GMT_PRIMARY]);
 		if (fore) {
-			gmtplot_vertical_wall (GMT, PSL, GMT->current.proj.z_project.quadrant + 3, nesw, false);
-			gmtplot_vertical_wall (GMT, PSL, GMT->current.proj.z_project.quadrant    , nesw, false);
+			gmtplot_vertical_wall (GMT, PSL, GMT->current.proj.z_project.quadrant + 3, nesw, false, GMT->current.map.frame.draw_box);
+			gmtplot_vertical_wall (GMT, PSL, GMT->current.proj.z_project.quadrant    , nesw, false, GMT->current.map.frame.draw_box);
 		}
 		if (back) {
-			gmtplot_vertical_wall (GMT, PSL, GMT->current.proj.z_project.quadrant + 1, nesw, true);
-			gmtplot_vertical_wall (GMT, PSL, GMT->current.proj.z_project.quadrant + 2, nesw, true);
+			gmtplot_vertical_wall (GMT, PSL, GMT->current.proj.z_project.quadrant + 1, nesw, true, GMT->current.map.frame.draw_box);
+			gmtplot_vertical_wall (GMT, PSL, GMT->current.proj.z_project.quadrant + 2, nesw, true, GMT->current.map.frame.draw_box);
+		}
+		if (GMT->current.map.frame.draw_box & GMT_3D_BOX) {
+			gmtplot_cube_box (GMT, PSL, GMT->current.proj.z_project.quadrant + 3, nesw);
+			gmtplot_cube_box (GMT, PSL, GMT->current.proj.z_project.quadrant    , nesw);
+			gmtplot_cube_box (GMT, PSL, GMT->current.proj.z_project.quadrant + 1, nesw);
+			gmtplot_cube_box (GMT, PSL, GMT->current.proj.z_project.quadrant + 2, nesw);
 		}
 	}
 
@@ -5540,6 +5625,7 @@ void gmt_vertical_axis (struct GMT_CTRL *GMT, unsigned int mode) {
 
 	if (fore && GMT->current.map.frame.side[Z_SIDE]) {
 		unsigned int k, n_z, quadrant, corner_to_quadrant[5] = {0, 2, 1, 4, 3}, z_axis[4];	/* Given corner ID 1-4, return quadrant, or vice versa (0 is unused) */
+		bool below;
 		gmt_M_memcpy (z_axis, GMT->current.map.frame.z_axis, 4, unsigned int);
 		for (k = n_z = 0; k < 4; k++)	/* Count # of vertical axes specified; if 0 then we do an auto-select */
 			if (z_axis[k]) n_z++;
@@ -5548,13 +5634,14 @@ void gmt_vertical_axis (struct GMT_CTRL *GMT, unsigned int mode) {
 		for (k = 0; k < 4; k++) {
 			if (z_axis[k] == 0) continue;	/* Not drawing this vertical axis */
 			quadrant = corner_to_quadrant[k+1];	/* Given corner (k+1), return quadrant */
+			below = gmtplot_z_axis_side (GMT, k, GMT->current.proj.z_project.quadrant);
 			gmt_xyz_to_xy (GMT, nesw[(quadrant/2*2+1)%4], nesw[((quadrant+1)/2*2)%4], GMT->common.R.wesn[ZLO], &xx, &yy);
 			/* Restrict reduced azimuth to -45 to 45 range */
 			az = GMT->current.proj.z_project.view_azimuth - 90.0 - floor ((GMT->current.proj.z_project.view_azimuth - 45.0) / 90.0) * 90.0;
 			PSL_command (PSL, "/PSL_GPP matrix currentmatrix def [%.12g %.12g %.12g %.12g %.12g %.12g] concat\n",
 				cosd(az), sind(az) * GMT->current.proj.z_project.sin_el, 0.0, GMT->current.proj.z_project.cos_el, xx * PSL->internal.x2ix, yy * PSL->internal.y2iy);
 			gmt_xy_axis (GMT, 0.0, -GMT->common.R.wesn[ZLO], GMT->current.proj.zmax - GMT->current.proj.zmin, GMT->common.R.wesn[ZLO],
-				GMT->common.R.wesn[ZHI], &GMT->current.map.frame.axis[GMT_Z], true, GMT->current.map.frame.side[Z_SIDE]);
+				GMT->common.R.wesn[ZHI], &GMT->current.map.frame.axis[GMT_Z], below, GMT->current.map.frame.side[Z_SIDE]);
 			PSL_command (PSL, "PSL_GPP setmatrix\n");
 		}
 	}
@@ -7578,10 +7665,10 @@ struct PSL_CTRL *gmt_plotinit (struct GMT_CTRL *GMT, struct GMT_OPTION *options)
 
 	PSL = GMT->PSL;	/* Shorthand */
 
-	if (GMT->current.map.frame.paint) {	/* Must squirrel this away for now since we may call psbasemap during the movie-indicators below */
+	if (GMT->current.map.frame.paint[GMT_Z]) {	/* Must squirrel this away for now since we may call psbasemap during the movie-indicators below */
 		do_paint = true;
-		gmt_M_memcpy (&fill, &GMT->current.map.frame.fill, 1U, struct GMT_FILL);
-		GMT->current.map.frame.paint = false;	/* Turn off for now */
+		gmt_M_memcpy (&fill, &GMT->current.map.frame.fill[GMT_Z], 1U, struct GMT_FILL);
+		GMT->current.map.frame.paint[GMT_Z] = false;	/* Turn off for now */
 	}
 
 	PSL->internal.verbose = GMT->current.setting.verbose;		/* Inherit verbosity level from GMT */
@@ -8024,21 +8111,21 @@ struct PSL_CTRL *gmt_plotinit (struct GMT_CTRL *GMT, struct GMT_OPTION *options)
 		PSL_command (PSL, "}!\n");
 	}
 	if (do_paint) {	/* Reset any canvas coloring here */
-		GMT->current.map.frame.paint = true;
-		gmt_M_memcpy (&GMT->current.map.frame.fill, &fill, 1U, struct GMT_FILL);
+		GMT->current.map.frame.paint[GMT_Z] = true;
+		gmt_M_memcpy (&GMT->current.map.frame.fill[GMT_Z], &fill, 1U, struct GMT_FILL);
 	}
 
 	return (PSL);
 }
 
 void gmt_plotcanvas (struct GMT_CTRL *GMT) {
-	if (GMT->current.map.frame.paint) {	/* Paint the inside of the map with specified fill */
+	if (GMT->current.map.frame.paint[GMT_Z]) {	/* Paint the inside of the map (xy plane) with specified fill */
 		double *x = NULL, *y = NULL;
 		uint64_t np;
 		bool donut;
-		PSL_comment (GMT->PSL, "Fill the canvas %s\n", gmtlib_putfill (GMT, &GMT->current.map.frame.fill));
+		PSL_comment (GMT->PSL, "Fill the canvas %s\n", gmtlib_putfill (GMT, &GMT->current.map.frame.fill[GMT_Z]));
 		np = gmt_map_clip_path (GMT, &x, &y, &donut);
-		gmt_setfill (GMT, &GMT->current.map.frame.fill, 0);
+		gmt_setfill (GMT, &GMT->current.map.frame.fill[GMT_Z], 0);
 		PSL_plotpolygon (GMT->PSL, x, y, (int)((1 + donut) * np));
 		gmt_M_free (GMT, x);
 		gmt_M_free (GMT, y);
diff --git a/src/gmt_project.h b/src/gmt_project.h
index 0f09e0181c9..2a4c4ad4a84 100644
--- a/src/gmt_project.h
+++ b/src/gmt_project.h
@@ -140,6 +140,12 @@ enum GMT_enum_zdown {GMT_ZDOWN_R = 0,	/* Default: Annotating radius */
 	GMT_ZDOWN_ZP	= 2,	/* Annotating planetary radius - r */
 	GMT_ZDOWN_ZR	= 3};	/* Annotating given radius - r */
 
+/* For drawing the 3-D backboard */
+enum GMT_enum_3Dmode {
+	GMT_3D_NONE = 0,	/* Default: No 3-D backboard */
+	GMT_3D_WALL	= 1,	/* Draw the backboard */
+	GMT_3D_BOX	= 2};	/* Draw the backboard and the 3-D wire box */
+
 /* gmt_M_is_periodic means the east and west meridians of a global map are separated */
 #define gmt_M_is_periodic(C) (gmt_M_is_cylindrical (C) || gmt_M_is_misc (C))
 
@@ -503,19 +509,21 @@ struct GMT_PLOT_AXIS {		/* Information for one time axis */
 struct GMT_PLOT_FRAME {		/* Various parameters for plotting of time axis boundaries */
 	struct GMT_PLOT_AXIS axis[3];	/* One each for x, y, and z */
 	char header[GMT_LEN256];	/* Plot title */
-	struct GMT_FILL fill;		/* Fill for the basemap inside, if paint == true */
+	struct GMT_FILL fill[3];		/* Fill for the basemap inside for planes x,y,z, if paint == true */
+	struct GMT_PEN pen;		/* Pen for the 3-D back wall outlines */
 	bool plotted_header;		/* true if header has been plotted */
 	bool init;			/* true if -B was used at all */
 	bool set;			/* true if -B was used to set any increments */
 	bool draw;			/* true if -B<int> was used, even -B0, as sign to draw axes */
 	bool drawz;			/* true if -B<int> was used, even -Bz0, as sign to draw z axes */
-	bool paint;			/* true if -B +g<fill> was used */
-	bool draw_box;			/* true if a 3-D Z-box is desired */
+	bool paint[3];			/* true if -B +x[<fill>], +y[<fill>], +g<fill> was used */
 	bool no_frame;			/* true if we just want gridlines but no frame, i.e +n was used */
 	bool check_side;		/* true if lon and lat annotations should be on x and y axis only */
 	bool primary;			/* true if current axis is primary, false if secondary */
 	bool set_both;			/* true if -B argument applies to both x and y axes */
 	bool obl_grid;			/* true if +o was given to draw oblique gridlines */
+	bool draw_wall;			/* true if +w was given to draw backwall outline */
+	unsigned int draw_box;			/* 0 = no 3-D frame. 1 if 3-D Z-box is desired [default], 2 if no -Z box lines covering up the plot */
 	unsigned int internal_annot;	/* 1 (longitude) or 2 (latitude or radius) if +i was given to draw internal annotations */
 	unsigned int set_frame[2];	/* 1 if a -B<WESNframe> setting was given */
 	unsigned int horizontal;	/* 1 is S/N annotations should be parallel to axes, 2 if forced */
diff --git a/src/grdimage.c b/src/grdimage.c
index 7bb1c7eb99f..2cc31908795 100644
--- a/src/grdimage.c
+++ b/src/grdimage.c
@@ -1260,9 +1260,9 @@ EXTERN_MSC int GMT_grdimage (void *V_API, int mode, void *args) {
 								   But what would it take to have a user selected bg color? */
 								double o, t;		/* o - opacity, t = transparency */
 								o = Img_proj->data[node_RGBA] / 255.0;	t = 1 - o;
-								rgb[0] = o * rgb[0] + t * GMT->current.map.frame.fill.rgb[0];
-								rgb[1] = o * rgb[1] + t * GMT->current.map.frame.fill.rgb[1];
-								rgb[2] = o * rgb[2] + t * GMT->current.map.frame.fill.rgb[2];
+								rgb[0] = o * rgb[0] + t * GMT->current.map.frame.fill[GMT_Z].rgb[0];
+								rgb[1] = o * rgb[1] + t * GMT->current.map.frame.fill[GMT_Z].rgb[1];
+								rgb[2] = o * rgb[2] + t * GMT->current.map.frame.fill[GMT_Z].rgb[2];
 								node_RGBA++;
 							}
 						}
diff --git a/src/psbasemap.c b/src/psbasemap.c
index e0c7b670827..72335ffd077 100644
--- a/src/psbasemap.c
+++ b/src/psbasemap.c
@@ -192,8 +192,8 @@ static int parse (struct GMT_CTRL *GMT, struct PSBASEMAP_CTRL *Ctrl, struct GMT_
 			case 'G':	/* Set canvas color */
 				if (gmt_M_compat_check (GMT, 4)) {
 					GMT_Report (API, GMT_MSG_COMPAT, "Option -G is deprecated; -B...+g%s was set instead, use this in the future.\n", opt->arg);
-					GMT->current.map.frame.paint = true;
-					if (gmt_getfill (GMT, opt->arg, &GMT->current.map.frame.fill)) {
+					GMT->current.map.frame.paint[GMT_Z] = true;
+					if (gmt_getfill (GMT, opt->arg, &GMT->current.map.frame.fill[GMT_Z])) {
 						gmt_fill_syntax (GMT, 'G', NULL, " ");
 						n_errors++;
 					}
diff --git a/src/pscoast.c b/src/pscoast.c
index 0557a777a0a..d99a50bedc1 100644
--- a/src/pscoast.c
+++ b/src/pscoast.c
@@ -149,8 +149,8 @@ static void *New_Ctrl (struct GMT_CTRL *GMT) {	/* Allocate and initialize a new
 
 	C->A.info.high = GSHHS_MAX_LEVEL;			/* Include all GSHHS levels */
 	C->D.set = 'l';						/* Low-resolution coastline data */
-	if (GMT->current.map.frame.paint)	/* Default Ocean color = Frame background color */
-		C->S.fill = GMT->current.map.frame.fill;
+	if (GMT->current.map.frame.paint[GMT_Z])	/* Default Ocean color = Frame background color */
+		C->S.fill = GMT->current.map.frame.fill[GMT_Z];
 	else
 		gmt_init_fill (GMT, &C->S.fill, 1.0, 1.0, 1.0);		/* Default Ocean color = white */
 	C->C.fill[LAKE] = C->C.fill[RIVER] = C->S.fill;		/* Default Lake/Riverlake color = Ocean color */
@@ -932,8 +932,8 @@ EXTERN_MSC int GMT_pscoast (void *V_API, int mode, void *args) {
 		clobber_background = true;
 		recursive = false;
 		if (!Ctrl->S.active) {	/* Since we are painting wet areas we must now reset them to white */
-			if (GMT->current.map.frame.paint)	/* Let ocean color match cancas fill color */
-				fill[0] = GMT->current.map.frame.fill;
+			if (GMT->current.map.frame.paint[GMT_Z])	/* Let ocean color match cancas fill color */
+				fill[0] = GMT->current.map.frame.fill[GMT_Z];
 			else
 				gmt_init_fill (GMT, &fill[0], 1.0, 1.0, 1.0);	/* Default Ocean color = white */
 		}
diff --git a/src/psrose.c b/src/psrose.c
index 56b1d305948..0b220dcb5bf 100644
--- a/src/psrose.c
+++ b/src/psrose.c
@@ -743,8 +743,8 @@ EXTERN_MSC int GMT_psrose (void *V_API, int mode, void *args) {
 		Return (GMT_PROJECTION_ERROR);
 	}
 
-	if (GMT->current.map.frame.paint) {	/* Until psrose uses a polar projection we must bypass the basemap fill and do it ourself here */
-		GMT->current.map.frame.paint = false;	/* Turn off so gmt_plotinit won't fill */
+	if (GMT->current.map.frame.paint[GMT_Z]) {	/* Until psrose uses a polar projection we must bypass the basemap fill and do it ourself here */
+		GMT->current.map.frame.paint[GMT_Z] = false;	/* Turn off so gmt_plotinit won't fill */
 		do_fill = true;
 	}
 	if ((PSL = gmt_plotinit (GMT, options)) == NULL) Return (GMT_RUNTIME_ERROR);
@@ -779,14 +779,14 @@ EXTERN_MSC int GMT_psrose (void *V_API, int mode, void *args) {
 
 	if (do_fill) {	/* Until psrose uses a polar projection we must bypass the basemap fill and do it ourself here */
 		double dim = 2.0 * Ctrl->S.scale;
-		GMT->current.map.frame.paint = true;	/* Restore original setting */
+		GMT->current.map.frame.paint[GMT_Z] = true;	/* Restore original setting */
 		if (half_only) {	/* Clip the bottom half of the circle */
 			double xc[4], yc[4];
 			xc[0] = xc[3] = -Ctrl->S.scale;	xc[1] = xc[2] = Ctrl->S.scale;
 			yc[0] = yc[1] = 0.0;	yc[2] = yc[3] = Ctrl->S.scale;
 			PSL_beginclipping (PSL, xc, yc, 4, GMT->session.no_rgb, 3);
 		}
-		gmt_setfill (GMT, &GMT->current.map.frame.fill, 0);
+		gmt_setfill (GMT, &GMT->current.map.frame.fill[GMT_Z], 0);
 		PSL_plotsymbol (PSL, 0.0, 0.0, &dim, PSL_CIRCLE);
 		if (half_only) PSL_endclipping (PSL, 1);		/* Reduce polygon clipping by one level */
 	}
diff --git a/src/psternary.c b/src/psternary.c
index 1201d7fbe92..635d56335b6 100644
--- a/src/psternary.c
+++ b/src/psternary.c
@@ -426,10 +426,10 @@ EXTERN_MSC int GMT_psternary (void *V_API, int mode, void *args) {
 	 * axis arguments.  We also must handle the canvas filling separately.  The three axis are 60 degrees
 	 * relative to each other and we do this directly with PSL calls. */
 
-	if (GMT->current.map.frame.paint) {	/* Paint the inside of the map with specified fill */
-		gmt_setfill (GMT, &GMT->current.map.frame.fill, 0);
+	if (GMT->current.map.frame.paint[GMT_Z]) {	/* Paint the inside of the map with specified fill */
+		gmt_setfill (GMT, &GMT->current.map.frame.fill[GMT_Z], 0);
 		PSL_plotpolygon (PSL, tri_x, tri_y, 4);
-		GMT->current.map.frame.paint = false;
+		GMT->current.map.frame.paint[GMT_Z] = false;
 	}
 	/* Count how many of the three sides will be drawn */
 	if (GMT->current.map.frame.side[S_SIDE]) n_sides++;	/* The bottom (a) side */