diff --git a/xarray/core/datatree.py b/xarray/core/datatree.py
index 267911a12a0..19bfd7130d5 100644
--- a/xarray/core/datatree.py
+++ b/xarray/core/datatree.py
@@ -1683,7 +1683,8 @@ def reduce(
                 numeric_only=numeric_only,
                 **kwargs,
             )
-            result[node.path] = node_result
+            path = "/" if node is self else node.relative_to(self)
+            result[path] = node_result
         return type(self).from_dict(result, name=self.name)
 
     def _selective_indexing(
@@ -1708,15 +1709,17 @@ def _selective_indexing(
             # Ideally, we would avoid creating such coordinates in the first
             # place, but that would require implementing indexing operations at
             # the Variable instead of the Dataset level.
-            for k in node_indexers:
-                if k not in node._node_coord_variables and k in node_result.coords:
-                    # We remove all inherited coordinates. Coordinates
-                    # corresponding to an index would be de-duplicated by
-                    # _deduplicate_inherited_coordinates(), but indexing (e.g.,
-                    # with a scalar) can also create scalar coordinates, which
-                    # need to be explicitly removed.
-                    del node_result.coords[k]
-            result[node.path] = node_result
+            if node is not self:
+                for k in node_indexers:
+                    if k not in node._node_coord_variables and k in node_result.coords:
+                        # We remove all inherited coordinates. Coordinates
+                        # corresponding to an index would be de-duplicated by
+                        # _deduplicate_inherited_coordinates(), but indexing (e.g.,
+                        # with a scalar) can also create scalar coordinates, which
+                        # need to be explicitly removed.
+                        del node_result.coords[k]
+            path = "/" if node is self else node.relative_to(self)
+            result[path] = node_result
         return type(self).from_dict(result, name=self.name)
 
     def isel(
diff --git a/xarray/tests/test_datatree.py b/xarray/tests/test_datatree.py
index c43f53a22c1..97fe8212c86 100644
--- a/xarray/tests/test_datatree.py
+++ b/xarray/tests/test_datatree.py
@@ -1651,7 +1651,18 @@ def test_isel_inherited(self):
         assert_equal(actual, expected)
 
         actual = tree.isel(x=slice(None))
-        assert_equal(actual, tree)
+
+        # TODO: re-enable after the fix to copy() from #9628 is submitted
+        # actual = tree.children["child"].isel(x=slice(None))
+        # expected = tree.children["child"].copy()
+        # assert_identical(actual, expected)
+
+        actual = tree.children["child"].isel(x=0)
+        expected = DataTree(
+            dataset=xr.Dataset({"foo": 3}, coords={"x": 1}),
+            name="child",
+        )
+        assert_identical(actual, expected)
 
     def test_sel(self):
         tree = DataTree.from_dict(
@@ -1667,7 +1678,14 @@ def test_sel(self):
             }
         )
         actual = tree.sel(x=2)
-        assert_equal(actual, expected)
+        assert_identical(actual, expected)
+
+        actual = tree.children["first"].sel(x=2)
+        expected = DataTree(
+            dataset=xr.Dataset({"a": 2}, coords={"x": 2}),
+            name="first",
+        )
+        assert_identical(actual, expected)
 
 
 class TestAggregations:
@@ -1739,6 +1757,16 @@ def test_dim_argument(self):
         ):
             dt.mean("invalid")
 
+    def test_subtree(self):
+        tree = DataTree.from_dict(
+            {
+                "/child": Dataset({"a": ("x", [1, 2])}),
+            }
+        )
+        expected = DataTree(dataset=Dataset({"a": 1.5}), name="child")
+        actual = tree.children["child"].mean()
+        assert_identical(expected, actual)
+
 
 class TestOps:
     def test_unary_op(self):