diff --git a/bgzf/index/index.go b/bgzf/index/index.go
index ee936c8..c8ef342 100644
--- a/bgzf/index/index.go
+++ b/bgzf/index/index.go
@@ -70,12 +70,9 @@ func (r *ChunkReader) Read(p []byte) (int, error) {
 	// blocked mode and so will stop there anyway.
 	want := int(r.chunks[0].End.Block)
 	if r.chunks[0].End.Block == 0 && r.chunks[0].End.File > last.End.File {
-		// Special case for when the current end block offset is zero.
-		// We pick an arbitrary length (the maximum progression).
-		// Because we must move past the current bgzf block to get
-		// to the current chunk end this is safe since the bgzf
-		// Reader is in blocked mode.
-		want = len(p)
+		// Special case for when the current end block offset
+		// is zero.
+		want = r.r.BlockLen()
 	}
 	var cursor int
 	if last.End.File == r.chunks[0].End.File {
diff --git a/bgzf/index/index_test.go b/bgzf/index/index_test.go
index 185eaff..903a36b 100644
--- a/bgzf/index/index_test.go
+++ b/bgzf/index/index_test.go
@@ -265,13 +265,9 @@ func (s *S) TestIssue10(c *check.C) {
 
 					var got bytes.Buffer
 					io.Copy(&got, cr)
-					gotString := got.String()
-					c.Check(strings.Contains(gotString, want), check.Equals, true,
+					c.Check(got.String(), check.Equals, want,
 						check.Commentf("clean=%t merge=%t trunc=%t chunks=%+v", clean, strategy != nil, truncFinal, chunks),
 					)
-					if gotString != want {
-						c.Logf("read over-run clean=%t merge=%t trunc=%t:\n\tgot: %q\n\twant:%q", clean, strategy != nil, truncFinal, gotString, want)
-					}
 				}
 			}
 		}
diff --git a/bgzf/reader.go b/bgzf/reader.go
index 7223e01..b513a14 100644
--- a/bgzf/reader.go
+++ b/bgzf/reader.go
@@ -487,6 +487,10 @@ func (bg *Reader) Seek(off Offset) error {
 // seek operation.
 func (bg *Reader) LastChunk() Chunk { return bg.lastChunk }
 
+// BlockLen returns the number of bytes remaining to be read from the
+// current BGZF block.
+func (bg *Reader) BlockLen() int { return bg.current.len() }
+
 // Close closes the reader and releases resources.
 func (bg *Reader) Close() error {
 	if bg.control != nil {
@@ -521,9 +525,6 @@ func (bg *Reader) Read(p []byte) (int, error) {
 	for n < len(p) && bg.err == nil {
 		var _n int
 		_n, bg.err = bg.current.Read(p[n:])
-		if _n > 0 {
-			bg.lastChunk.End = bg.current.txOffset()
-		}
 		n += _n
 		if bg.err == io.EOF {
 			if n == len(p) {
@@ -533,6 +534,7 @@ func (bg *Reader) Read(p []byte) (int, error) {
 
 			if bg.Blocked {
 				bg.err = nil
+				bg.lastChunk.End = bg.current.txOffset()
 				return n, io.EOF
 			}
 
@@ -543,6 +545,7 @@ func (bg *Reader) Read(p []byte) (int, error) {
 		}
 	}
 
+	bg.lastChunk.End = bg.current.txOffset()
 	return n, bg.err
 }