diff --git a/pandas/core/indexing.py b/pandas/core/indexing.py
index f8578d87e4cad..7681ac588d3ca 100644
--- a/pandas/core/indexing.py
+++ b/pandas/core/indexing.py
@@ -825,7 +825,15 @@ def _getitem_lowerdim(self, tup: tuple):
         ax0 = self.obj._get_axis(0)
         # ...but iloc should handle the tuple as simple integer-location
         # instead of checking it as multiindex representation (GH 13797)
-        if isinstance(ax0, MultiIndex) and self.name != "iloc":
+        if (
+            isinstance(ax0, MultiIndex)
+            and self.name != "iloc"
+            and not any(isinstance(x, slice) for x in tup)
+        ):
+            # Note: in all extant test cases, replacing the slice condition with
+            #  `all(is_hashable(x) or com.is_null_slice(x) for x in tup)`
+            #  is equivalent.
+            #  (see the other place where we call _handle_lowerdim_multi_index_axis0)
             with suppress(IndexingError):
                 return self._handle_lowerdim_multi_index_axis0(tup)
 
@@ -879,7 +887,7 @@ def _getitem_nested_tuple(self, tup: tuple):
             ):
                 # GH#35349 Raise if tuple in tuple for series
                 raise ValueError("Too many indices")
-            if self.ndim == 1 or not any(isinstance(x, slice) for x in tup):
+            if all(is_hashable(x) or com.is_null_slice(x) for x in tup):
                 # GH#10521 Series should reduce MultiIndex dimensions instead of
                 #  DataFrame, IndexingError is not raised when slice(None,None,None)
                 #  with one row.
@@ -1117,16 +1125,16 @@ def _handle_lowerdim_multi_index_axis0(self, tup: tuple):
         try:
             # fast path for series or for tup devoid of slices
             return self._get_label(tup, axis=axis)
-        except (TypeError, InvalidIndexError):
+        except TypeError as err:
             # slices are unhashable
-            pass
+            raise IndexingError("No label returned") from err
+
         except KeyError as ek:
             # raise KeyError if number of indexers match
             # else IndexingError will be raised
             if self.ndim < len(tup) <= self.obj.index.nlevels:
                 raise ek
-
-        raise IndexingError("No label returned")
+            raise IndexingError("No label returned") from ek
 
     def _getitem_axis(self, key, axis: int):
         key = item_from_zerodim(key)
diff --git a/pandas/tests/indexing/multiindex/test_getitem.py b/pandas/tests/indexing/multiindex/test_getitem.py
index f1fbe0c5a6b9c..3790a6e9a5319 100644
--- a/pandas/tests/indexing/multiindex/test_getitem.py
+++ b/pandas/tests/indexing/multiindex/test_getitem.py
@@ -28,9 +28,11 @@ def test_series_getitem_multiindex(access_method, level1_value, expected):
     # GH 6018
     # series regression getitem with a multi-index
 
-    s = Series([1, 2, 3])
-    s.index = MultiIndex.from_tuples([(0, 0), (1, 1), (2, 1)])
-    result = access_method(s, level1_value)
+    mi = MultiIndex.from_tuples([(0, 0), (1, 1), (2, 1)], names=["A", "B"])
+    ser = Series([1, 2, 3], index=mi)
+    expected.index.name = "A"
+
+    result = access_method(ser, level1_value)
     tm.assert_series_equal(result, expected)
 
 
diff --git a/pandas/tests/indexing/multiindex/test_loc.py b/pandas/tests/indexing/multiindex/test_loc.py
index afcff6db5e3dd..bc59c51e359ae 100644
--- a/pandas/tests/indexing/multiindex/test_loc.py
+++ b/pandas/tests/indexing/multiindex/test_loc.py
@@ -787,10 +787,10 @@ def test_loc_getitem_index_differently_ordered_slice_none_duplicates(indexer):
 
 
 def test_loc_getitem_drops_levels_for_one_row_dataframe():
-    # GH#10521
+    # GH#10521 "x" and "z" are both scalar indexing, so those levels are dropped
     mi = MultiIndex.from_arrays([["x"], ["y"], ["z"]], names=["a", "b", "c"])
     df = DataFrame({"d": [0]}, index=mi)
-    expected = df.copy()
+    expected = df.droplevel([0, 2])
     result = df.loc["x", :, "z"]
     tm.assert_frame_equal(result, expected)