diff --git a/src/transformnd/spaced.py b/src/transformnd/spaced.py
index ee93f4f..2bb466c 100644
--- a/src/transformnd/spaced.py
+++ b/src/transformnd/spaced.py
@@ -38,7 +38,7 @@ def invert(self) -> Self | None:
         t = self.transform.invert()
         if t is None:
             return None
-        return type(self)(t, self.spaces.source, self.spaces.target)
+        return type(self)(t, self.spaces.target, self.spaces.source)
 
     def __invert__(self):
         out = self.invert()
diff --git a/tests/transforms/test_project_axis.py b/tests/transforms/test_project_axis.py
index 545c684..5c9eb33 100644
--- a/tests/transforms/test_project_axis.py
+++ b/tests/transforms/test_project_axis.py
@@ -25,6 +25,22 @@ def test_invert():
     assert ti.created == {0}
 
 
+def test_change_ndim():
+    orig = as_floats([[1, 2]])
+    add0 = ProjectAxis(created={0}, source_ndim=2)
+    assert add0.ndims.source == 2
+    assert add0.ndims.target == 3
+    added = add0.apply(orig)
+    assert added == pytest.approx(as_floats([[0, 1, 2]]))
+
+    rem0 = add0.invert()
+    assert rem0 is not None
+    assert rem0.ndims.source == 3
+    assert rem0.ndims.target == 2
+    removed = rem0.apply(added)
+    assert removed == pytest.approx(orig)
+
+
 def random_ops(in_ndim: int, out_ndim: int, seed=1991) -> ProjectAxis:
     rng = Random(seed)
     n_dropped = rng.randint(max(0, in_ndim - out_ndim), in_ndim - 1)
diff --git a/tests/transforms/test_spaced.py b/tests/transforms/test_spaced.py
new file mode 100644
index 0000000..07a30d8
--- /dev/null
+++ b/tests/transforms/test_spaced.py
@@ -0,0 +1,15 @@
+import pytest
+from transformnd.spaced import Spaced
+from transformnd.transforms import Translate
+from transformnd.util import as_floats
+
+
+def test_invert_spaced(coords5x3):
+    t1 = Translate(as_floats([1, 2, 3]))
+    s1 = Spaced(t1, "a", "b")
+    s2 = s1.invert()
+    assert s2 is not None
+    assert s2.spaces.source == s1.spaces.target
+    assert s2.spaces.target == s1.spaces.source
+
+    assert s2.transform.apply(s1.transform.apply(coords5x3)) == pytest.approx(coords5x3)