diff --git a/python/cudf/cudf/tests/test_multiindex.py b/python/cudf/cudf/tests/test_multiindex.py
index 465cf36e1f3..80f44065e9f 100644
--- a/python/cudf/cudf/tests/test_multiindex.py
+++ b/python/cudf/cudf/tests/test_multiindex.py
@@ -5,7 +5,9 @@
 """
 import itertools
 import operator
+import pickle
 import re
+from io import BytesIO
 
 import cupy as cp
 import numpy as np
@@ -1553,3 +1555,49 @@ def test_multiIndex_duplicate_names():
     )
 
     assert_eq(gi, pi)
+
+
+@pytest.mark.parametrize(
+    "names",
+    [
+        ["a", "b", "c"],
+        [None, None, None],
+        ["aa", "aa", "aa"],
+        ["bb", "aa", "aa"],
+        None,
+    ],
+)
+def test_pickle_roundtrip_multiIndex(names):
+    df = cudf.DataFrame(
+        {
+            "one": [1, 2, 3],
+            "two": [True, False, True],
+            "three": ["ab", "cd", "ef"],
+            "four": [0.2, 0.1, -10.2],
+        }
+    )
+    expected_df = df.set_index(["one", "two", "three"])
+    expected_df.index.names = names
+    local_file = BytesIO()
+
+    pickle.dump(expected_df, local_file)
+    local_file.seek(0)
+    actual_df = pickle.load(local_file)
+    assert_eq(expected_df, actual_df)
+
+
+def test_difference():
+    midx = cudf.MultiIndex(
+        levels=[[1, 3, 4, 5], [1, 2, 5]],
+        codes=[[0, 0, 1, 2, 3], [0, 2, 1, 1, 0]],
+        names=["x", "y"],
+    )
+    midx2 = cudf.MultiIndex(
+        levels=[[1, 3, 4, 5], [1, 2, 5]],
+        codes=[[0, 0, 1, 2, 3, 3], [0, 2, 1, 1, 0, 2]],
+        names=["x", "y"],
+    )
+
+    expected = midx2.to_pandas().difference(midx.to_pandas())
+    actual = midx2.difference(midx)
+    assert_eq(expected, actual)