diff --git a/glue/core/state.py b/glue/core/state.py
index 333f9ffc8..47f9f1d68 100644
--- a/glue/core/state.py
+++ b/glue/core/state.py
@@ -65,7 +65,7 @@ def load(rec, context)
 import numpy as np
 from matplotlib.colors import Colormap
 from matplotlib import cm
-from astropy.units import NamedUnit, Unit
+from astropy.units import UnitBase, Unit
 from astropy.wcs import WCS
 import shapely
 
@@ -622,14 +622,15 @@ def _load_slice(rec, context):
     return slice(rec['start'], rec['stop'], rec['step'])
 
 
-@saver(NamedUnit)
-def _save_named_unit(unit, context):
-    return dict(named_unit=unit.to_string())
+@saver(UnitBase)
+def _save_unit_base(unit, context):
+    return dict(unit_base=unit.to_string())
 
 
-@loader(NamedUnit)
-def _load_named_unit(rec, context):
-    return Unit(rec["named_unit"])
+@loader(UnitBase)
+def _load_unit_base(rec, context):
+    return Unit(rec["unit_base"])
+
 
 
 @saver(WCS)
diff --git a/glue/core/tests/test_state.py b/glue/core/tests/test_state.py
index c2be7e0b0..3656f83b0 100644
--- a/glue/core/tests/test_state.py
+++ b/glue/core/tests/test_state.py
@@ -312,6 +312,21 @@ def test_astropy_units():
     unit2 = clone(unit)
     assert unit2 is unit
 
+    unit = u.km
+    unit2 = clone(unit)
+    assert unit2 is unit
+
+
+@requires_astropy
+def test_astropy_compound_units():
+    import astropy.units as u
+    unit = u.m / u.s
+    unit2 = clone(unit)
+    assert unit2 == unit
+    unit = u.W / u.m**2 / u.nm
+    unit2 = clone(unit)
+    assert unit2 == unit
+
 
 class DummyClass(object):
     pass