diff --git a/pandas-stubs/core/indexes/base.pyi b/pandas-stubs/core/indexes/base.pyi
index 1f53b8b3..eff99f92 100644
--- a/pandas-stubs/core/indexes/base.pyi
+++ b/pandas-stubs/core/indexes/base.pyi
@@ -42,7 +42,6 @@ from pandas._typing import (
     Label,
     Level,
     NaPosition,
-    Scalar,
     np_ndarray_anyint,
     np_ndarray_bool,
     np_ndarray_int64,
@@ -193,7 +192,7 @@ class Index(IndexOpsMixin[S1], PandasObject):
     def __nonzero__(self) -> None: ...
     __bool__ = ...
     def union(self, other: list[HashableT] | Index, sort=...) -> Index: ...
-    def intersection(self, other: list[T1] | Self, sort: bool = ...) -> Self: ...
+    def intersection(self, other: list[T1] | Index, sort: bool = ...) -> Self: ...
     def difference(self, other: list | Index, sort: bool | None = None) -> Self: ...
     def symmetric_difference(
         self, other: list[T1] | Index, result_name=..., sort=...
@@ -264,12 +263,12 @@ class Index(IndexOpsMixin[S1], PandasObject):
     def shape(self) -> tuple[int, ...]: ...
     # Extra methods from old stubs
     def __eq__(self, other: object) -> np_ndarray_bool: ...  # type: ignore[override]
-    def __iter__(self) -> Iterator: ...
+    def __iter__(self) -> Iterator[S1]: ...
     def __ne__(self, other: object) -> np_ndarray_bool: ...  # type: ignore[override]
-    def __le__(self, other: Index | Scalar) -> np_ndarray_bool: ...  # type: ignore[override]
-    def __ge__(self, other: Index | Scalar) -> np_ndarray_bool: ...  # type: ignore[override]
-    def __lt__(self, other: Index | Scalar) -> np_ndarray_bool: ...  # type: ignore[override]
-    def __gt__(self, other: Index | Scalar) -> np_ndarray_bool: ...  # type: ignore[override]
+    def __le__(self, other: Self | S1) -> np_ndarray_bool: ...  # type: ignore[override]
+    def __ge__(self, other: Self | S1) -> np_ndarray_bool: ...  # type: ignore[override]
+    def __lt__(self, other: Self | S1) -> np_ndarray_bool: ...  # type: ignore[override]
+    def __gt__(self, other: Self | S1) -> np_ndarray_bool: ...  # type: ignore[override]
     # overwrite inherit methods from OpsMixin
     @overload
     def __mul__(  # type: ignore[misc]
diff --git a/tests/test_indexes.py b/tests/test_indexes.py
index 80ec5b3b..90b9bcbe 100644
--- a/tests/test_indexes.py
+++ b/tests/test_indexes.py
@@ -25,16 +25,6 @@
 
 if TYPE_CHECKING:
     MYPY_CHECKING: bool = True
-    # See test_sorted_and_list() where mypy and pyright do different
-    # inference on sorted(pd.Index)
-    if MYPY_CHECKING:
-        from typing import Any
-
-        from typing_extensions import TypeAlias
-
-        SupportsRichComparison: TypeAlias = Any
-    else:
-        from _typeshed import SupportsRichComparison  # noqa: F401
 
 
 def test_index_unique() -> None:
@@ -719,22 +709,11 @@ def test_interval_index_tuples():
 def test_sorted_and_list() -> None:
     # GH 497
     i1 = pd.Index([3, 2, 1])
-    # mypy infers sorted(i1) as list[Any], while pyright infers sorted(i1) as
-    # list[SupportsRichComparison]
     check(
-        assert_type(
-            sorted(i1),
-            "list[SupportsRichComparison]",
-        ),
-        list,
-    )
-    check(
-        assert_type(
-            list(i1),
-            list,
-        ),
+        assert_type(sorted(i1), list[int]),
         list,
     )
+    check(assert_type(list(i1), list[int]), list)
 
 
 def test_index_operators() -> None: