diff --git a/pandas/tests/indexes/multi/test_setops.py b/pandas/tests/indexes/multi/test_setops.py
index 5d1efea657426..57c4af1a0fe1c 100644
--- a/pandas/tests/indexes/multi/test_setops.py
+++ b/pandas/tests/indexes/multi/test_setops.py
@@ -544,3 +544,24 @@ def test_union_duplicates(index, request):
 
     result = mi2.union(mi1)
     tm.assert_index_equal(result, mi2.sort_values())
+
+
+@pytest.mark.parametrize(
+    "levels1, levels2, codes1, codes2, names",
+    [
+        (
+            [["a", "b", "c"], [0, ""]],
+            [["c", "d", "b"], [""]],
+            [[0, 1, 2], [1, 1, 1]],
+            [[0, 1, 2], [0, 0, 0]],
+            ["name1", "name2"],
+        ),
+    ],
+)
+def test_intersection_lexsort_depth(levels1, levels2, codes1, codes2, names):
+    # GH#25169
+    mi1 = MultiIndex(levels=levels1, codes=codes1, names=names)
+    mi2 = MultiIndex(levels=levels2, codes=codes2, names=names)
+    mi_int = mi1.intersection(mi2)
+
+    assert mi_int.lexsort_depth == 0
diff --git a/pandas/tests/indexing/test_loc.py b/pandas/tests/indexing/test_loc.py
index 01dfeaef1a5a1..4c38a2219372d 100644
--- a/pandas/tests/indexing/test_loc.py
+++ b/pandas/tests/indexing/test_loc.py
@@ -25,6 +25,7 @@
     IndexSlice,
     MultiIndex,
     Period,
+    PeriodIndex,
     Series,
     SparseDtype,
     Timedelta,
@@ -2876,6 +2877,22 @@ def test_loc_set_int_dtype():
     tm.assert_frame_equal(df, expected)
 
 
+def test_loc_periodindex_3_levels():
+    # GH#24091
+    p_index = PeriodIndex(
+        ["20181101 1100", "20181101 1200", "20181102 1300", "20181102 1400"],
+        name="datetime",
+        freq="B",
+    )
+    mi_series = DataFrame(
+        [["A", "B", 1.0], ["A", "C", 2.0], ["Z", "Q", 3.0], ["W", "F", 4.0]],
+        index=p_index,
+        columns=["ONE", "TWO", "VALUES"],
+    )
+    mi_series = mi_series.set_index(["ONE", "TWO"], append=True)["VALUES"]
+    assert mi_series.loc[(p_index[0], "A", "B")] == 1.0
+
+
 class TestLocSeries:
     @pytest.mark.parametrize("val,expected", [(2**63 - 1, 3), (2**63, 4)])
     def test_loc_uint64(self, val, expected):