diff --git a/pandas/tests/frame/methods/test_rename.py b/pandas/tests/frame/methods/test_rename.py
index 1581bc8a0c70b..33fb191027c27 100644
--- a/pandas/tests/frame/methods/test_rename.py
+++ b/pandas/tests/frame/methods/test_rename.py
@@ -184,14 +184,16 @@ def test_rename_inplace(self, float_frame):
         assert "C" in float_frame
         assert "foo" not in float_frame
 
-        c_id = id(float_frame["C"])
+        c_values = float_frame["C"]
         float_frame = float_frame.copy()
         return_value = float_frame.rename(columns={"C": "foo"}, inplace=True)
         assert return_value is None
 
         assert "C" not in float_frame
         assert "foo" in float_frame
-        assert id(float_frame["foo"]) != c_id
+        # GH 44153
+        # Used to be id(float_frame["foo"]) != c_id, but flaky in the CI
+        assert float_frame["foo"] is not c_values
 
     def test_rename_bug(self):
         # GH 5344
diff --git a/pandas/tests/frame/methods/test_sort_index.py b/pandas/tests/frame/methods/test_sort_index.py
index 71822628473f4..1556a9507ab9e 100644
--- a/pandas/tests/frame/methods/test_sort_index.py
+++ b/pandas/tests/frame/methods/test_sort_index.py
@@ -224,13 +224,15 @@ def test_sort_index_inplace(self):
 
         # axis=0
         unordered = frame.loc[[3, 2, 4, 1]]
-        a_id = id(unordered["A"])
+        a_values = unordered["A"]
         df = unordered.copy()
         return_value = df.sort_index(inplace=True)
         assert return_value is None
         expected = frame
         tm.assert_frame_equal(df, expected)
-        assert a_id != id(df["A"])
+        # GH 44153 related
+        # Used to be a_id != id(df["A"]), but flaky in the CI
+        assert a_values is not df["A"]
 
         df = unordered.copy()
         return_value = df.sort_index(ascending=False, inplace=True)