diff --git a/xarray/core/alignment.py b/xarray/core/alignment.py
index b4fee1773b8..a905dd37b35 100644
--- a/xarray/core/alignment.py
+++ b/xarray/core/alignment.py
@@ -374,7 +374,13 @@ def is_alignable(obj):
         elif is_dict_like(variables):
             current_out = OrderedDict()
             for k, v in variables.items():
-                if is_alignable(v):
+                if is_alignable(v) and k not in indexes:
+                    # Skip variables in indexes for alignment, because these
+                    # should to be overwritten instead:
+                    # https://github.com/pydata/xarray/issues/725
+                    # https://github.com/pydata/xarray/issues/3377
+                    # TODO(shoyer): doing this here feels super-hacky -- can we
+                    # move it explicitly into merge instead?
                     positions.append(position)
                     keys.append(k)
                     targets.append(v)
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index fdd5a419383..e9efd5e7254 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -3047,6 +3047,21 @@ def test_setitem_auto_align(self):
         expected = Dataset({"x": ("y", [4, 5, 6])}, {"y": range(3)})
         assert_identical(ds, expected)
 
+    def test_setitem_dimension_override(self):
+        # regression test for GH-3377
+        ds = xr.Dataset({"x": [0, 1, 2]})
+        ds["x"] = ds["x"][:2]
+        expected = Dataset({"x": [0, 1]})
+        assert_identical(ds, expected)
+
+        ds = xr.Dataset({"x": [0, 1, 2]})
+        ds["x"] = np.array([0, 1])
+        assert_identical(ds, expected)
+
+        ds = xr.Dataset({"x": [0, 1, 2]})
+        ds.coords["x"] = [0, 1]
+        assert_identical(ds, expected)
+
     def test_setitem_with_coords(self):
         # Regression test for GH:2068
         ds = create_test_data()