diff --git a/lib/iris/fileformats/__init__.py b/lib/iris/fileformats/__init__.py
index 8bfdb23b34..840487cf21 100644
--- a/lib/iris/fileformats/__init__.py
+++ b/lib/iris/fileformats/__init__.py
@@ -95,7 +95,12 @@ def _load_grib(*args, **kwargs):
 #
 FORMAT_AGENT.add_spec(
     FormatSpecification(
-        "NetCDF", MagicNumber(4), 0x43444601, netcdf.load_cubes, priority=5
+        "NetCDF",
+        MagicNumber(4),
+        0x43444601,
+        netcdf.load_cubes,
+        priority=5,
+        constraint_aware_handler=True,
     )
 )
 
@@ -107,6 +112,7 @@ def _load_grib(*args, **kwargs):
         0x43444602,
         netcdf.load_cubes,
         priority=5,
+        constraint_aware_handler=True,
     )
 )
 
@@ -119,6 +125,7 @@ def _load_grib(*args, **kwargs):
         0x894844460D0A1A0A,
         netcdf.load_cubes,
         priority=5,
+        constraint_aware_handler=True,
     )
 )
 
@@ -129,6 +136,7 @@ def _load_grib(*args, **kwargs):
     lambda protocol: protocol in ["http", "https"],
     netcdf.load_cubes,
     priority=6,
+    constraint_aware_handler=True,
 )
 FORMAT_AGENT.add_spec(_nc_dap)
 del _nc_dap
diff --git a/lib/iris/fileformats/netcdf.py b/lib/iris/fileformats/netcdf.py
index 00a207b86d..d07913bea8 100644
--- a/lib/iris/fileformats/netcdf.py
+++ b/lib/iris/fileformats/netcdf.py
@@ -38,6 +38,7 @@
     OceanSg2Factory,
 )
 import iris.config
+import iris._constraints
 import iris.coord_systems
 import iris.coords
 import iris.cube
@@ -780,7 +781,33 @@ def coord_from_term(term):
         cube.add_aux_factory(factory)
 
 
-def load_cubes(filenames, callback=None):
+def translate_constraints_to_var_callback(constraints):
+    """
+    Translate load constraints into a simple data-var filter function, if possible.
+
+    Returns:
+         * function(cf_var:CFDataVariable): --> bool,
+            or None.
+
+    For now, ONLY handles a single NameConstraint with no 'STASH' component.
+
+    """
+    constraints = iris._constraints.list_of_constraints(constraints)
+    result = None
+    if len(constraints) == 1:
+        (constraint,) = constraints
+        if (
+            isinstance(constraint, iris._constraints.NameConstraint)
+            and constraint.STASH == "none"
+        ):
+            # As long as it doesn't use a STASH match, then we can treat it as
+            # a testing against name properties of cf_var , so we can call its
+            # 'cube+func' passing the cf_var, as if the cf_var were a cube.
+            result = constraint._cube_func
+    return result
+
+
+def load_cubes(filenames, callback=None, constraints=None):
     """
     Loads cubes from a list of NetCDF filenames/URLs.
 
@@ -798,6 +825,9 @@ def load_cubes(filenames, callback=None):
         Generator of loaded NetCDF :class:`iris.cube.Cube`.
 
     """
+    # Create a low-level data-var filter from the original load constraints, if they are suitable.
+    var_callback = translate_constraints_to_var_callback(constraints)
+
     # TODO: rationalise UGRID/mesh handling once experimental.ugrid is folded
     #  into standard behaviour.
     # Deferred import to avoid circular imports.
@@ -836,6 +866,10 @@ def load_cubes(filenames, callback=None):
             cf.cf_group.promoted.values()
         )
         for cf_var in data_variables:
+            if var_callback and not var_callback(cf_var):
+                # Deliver only selected results.
+                continue
+
             # cf_var-specific mesh handling, if a mesh is present.
             # Build the mesh_coords *before* loading the cube - avoids
             # mesh-related attributes being picked up by