diff --git a/sharrow/aster.py b/sharrow/aster.py
index fe970ee..8762b27 100755
--- a/sharrow/aster.py
+++ b/sharrow/aster.py
@@ -408,7 +408,9 @@ def _replacement(
                 if self.get_default or (
                     topname == pref_topname and not self.swallow_errors
                 ):
-                    raise KeyError(f"{topname}..{attr}\nexpression={self.original_expr}")
+                    raise KeyError(
+                        f"{topname}..{attr}\nexpression={self.original_expr}"
+                    )
                 # we originally raised a KeyError here regardless, but what if
                 # we just give back the original node, and see if other spaces,
                 # possibly fallback spaces, might work?  If nothing works then
@@ -1010,6 +1012,16 @@ def visit_Compare(self, node):
                             f"\ncategories: {left_dictionary}",
                             stacklevel=2,
                         )
+                        # at this point, the right value is not in the left's categories, so
+                        # it is guaranteed to be not equal to any of the categories.
+                        if isinstance(node.ops[0], ast.Eq):
+                            result = ast.Constant(False)
+                        elif isinstance(node.ops[0], ast.NotEq):
+                            result = ast.Constant(True)
+                        else:
+                            raise ValueError(
+                                f"unexpected operator {node.ops[0]}"
+                            ) from None
                     if right_decoded is not None:
                         result = ast.Compare(
                             left=left.slice,
@@ -1043,6 +1055,16 @@ def visit_Compare(self, node):
                             f"\ncategories: {right_dictionary}",
                             stacklevel=2,
                         )
+                        # at this point, the left value is not in the right's categories, so
+                        # it is guaranteed to be not equal to any of the categories.
+                        if isinstance(node.ops[0], ast.Eq):
+                            result = ast.Constant(False)
+                        elif isinstance(node.ops[0], ast.NotEq):
+                            result = ast.Constant(True)
+                        else:
+                            raise ValueError(
+                                f"unexpected operator {node.ops[0]}"
+                            ) from None
                     if left_decoded is not None:
                         result = ast.Compare(
                             left=ast_Constant(left_decoded),
diff --git a/sharrow/tests/test_categorical.py b/sharrow/tests/test_categorical.py
index c5ab0b1..cd2a4e0 100644
--- a/sharrow/tests/test_categorical.py
+++ b/sharrow/tests/test_categorical.py
@@ -177,6 +177,48 @@ def test_missing_categorical():
     a = a.isel(expressions=0)
     assert all(a == np.asarray([1, 0, 1, 1, 1, 1]))
 
+    expr = "df.TourMode2 != 'BAD'"
+    with pytest.warns(UserWarning):
+        f8 = tree.setup_flow({expr: expr}, with_root_node_name="df")
+    a = f8.load_dataarray(dtype=np.int8)
+    a = a.isel(expressions=0)
+    assert all(a == np.asarray([1, 1, 1, 1, 1, 1]))
+
+    expr = "'BAD' != df.TourMode2"
+    with pytest.warns(UserWarning):
+        f9 = tree.setup_flow({expr: expr}, with_root_node_name="df")
+    a = f9.load_dataarray(dtype=np.int8)
+    a = a.isel(expressions=0)
+    assert all(a == np.asarray([1, 1, 1, 1, 1, 1]))
+
+    expr = "(df.TourMode2 == 'BAD') * 2"
+    with pytest.warns(UserWarning):
+        fA = tree.setup_flow({expr: expr}, with_root_node_name="df")
+    a = fA.load_dataarray(dtype=np.int8)
+    a = a.isel(expressions=0)
+    assert all(a == np.asarray([0, 0, 0, 0, 0, 0]))
+
+    expr = "(df.TourMode2 == 'BAD') * 2.2"
+    with pytest.warns(UserWarning):
+        fB = tree.setup_flow({expr: expr}, with_root_node_name="df")
+    a = fB.load_dataarray(dtype=np.int8)
+    a = a.isel(expressions=0)
+    assert all(a == np.asarray([0, 0, 0, 0, 0, 0]))
+
+    expr = "np.exp(df.TourMode2 == 'BAD') * 2.2"
+    with pytest.warns(UserWarning):
+        fC = tree.setup_flow({expr: expr}, with_root_node_name="df")
+    a = fC.load_dataarray(dtype=np.float32)
+    a = a.isel(expressions=0)
+    assert all(a == np.asarray([2.2, 2.2, 2.2, 2.2, 2.2, 2.2], dtype=np.float32))
+
+    expr = "(df.TourMode2 != 'BAD') * 2"
+    with pytest.warns(UserWarning):
+        fD = tree.setup_flow({expr: expr}, with_root_node_name="df")
+    a = fD.load_dataarray(dtype=np.int8)
+    a = a.isel(expressions=0)
+    assert all(a == np.asarray([2, 2, 2, 2, 2, 2]))
+
 
 def test_categorical_indexing(tours_dataset: xr.Dataset, skims_dataset: xr.Dataset):
     tree = sharrow.DataTree(tours=tours_dataset)