diff --git a/Changelog.rst b/Changelog.rst
index e8678dc686..310e2a5cd9 100644
--- a/Changelog.rst
+++ b/Changelog.rst
@@ -3,6 +3,8 @@ version 3.17.0
 
 **2024-??-??**
 
+* New keyword parameter to `cf.Field.insert_dimension`:
+  ``constructs`` (https://github.com/NCAS-CMS/cf-python/issues/719)
 * Added the ``cell_measures`` and ``coordinates`` keyword arguments to
   `cf.Field.weights`
   (https://github.com/NCAS-CMS/cf-python/issues/709)
diff --git a/cf/field.py b/cf/field.py
index a87ea84afb..cd5dcc3729 100644
--- a/cf/field.py
+++ b/cf/field.py
@@ -8687,7 +8687,9 @@ def _update_cell_methods(
             )  # pragma: no cover
 
     @_inplace_enabled(default=False)
-    def insert_dimension(self, axis, position=0, inplace=False):
+    def insert_dimension(
+        self, axis, position=0, constructs=False, inplace=False
+    ):
         """Insert a size 1 axis into the data array.
 
         .. versionadded:: 3.0.0
@@ -8712,6 +8714,13 @@ def insert_dimension(self, axis, position=0, inplace=False):
                 data array. By default the new axis has position 0, the
                 slowest varying position.
 
+            constructs: `bool`, optional
+                If True then also insert the new axis into all
+                metadata constructs that don't already include it. By
+                default, metadata constructs are not changed.
+
+                .. versionadded:: 3.17.0
+
             {{inplace: `bool`, optional}}
 
         :Returns:
@@ -8755,24 +8764,13 @@ def insert_dimension(self, axis, position=0, inplace=False):
                         : time(1) = [2019-01-01 00:00:00]
 
         """
-        f = _inplace_enabled_define_and_cleanup(self)
-
-        if axis is None:
-            axis = f.set_construct(self._DomainAxis(1))
-        else:
-            axis = f.domain_axis(
-                axis,
-                key=True,
-                default=ValueError("Can't identify a unique axis to insert"),
-            )
-
-        # Expand the dims in the field construct's data array
-        super(Field, f).insert_dimension(
-            axis=axis, position=position, inplace=True
+        return super().insert_dimension(
+            axis=axis,
+            position=position,
+            constructs=constructs,
+            inplace=inplace,
         )
 
-        return f
-
     def indices(self, *mode, **kwargs):
         """Create indices that define a subspace of the field construct.
 
diff --git a/cf/test/test_Field.py b/cf/test/test_Field.py
index 449fd32980..0bdece56c7 100644
--- a/cf/test/test_Field.py
+++ b/cf/test/test_Field.py
@@ -1143,6 +1143,10 @@ def test_Field_insert_dimension(self):
         self.assertEqual(g.ndim, f.ndim + 1)
         self.assertEqual(g.get_data_axes()[1:], f.get_data_axes())
 
+        self.assertEqual(g.cell_measure().ndim, 2)
+        h = g.insert_dimension(None, constructs=True)
+        self.assertEqual(h.cell_measure().ndim, 3)
+
         with self.assertRaises(ValueError):
             f.insert_dimension(1, "qwerty")