diff --git a/pandas-stubs/core/indexes/base.pyi b/pandas-stubs/core/indexes/base.pyi
index e29561eb3..584548d97 100644
--- a/pandas-stubs/core/indexes/base.pyi
+++ b/pandas-stubs/core/indexes/base.pyi
@@ -351,7 +351,7 @@ class Index(IndexOpsMixin[S1], ElementOpsMixin[S1]):
         Index,
     ]: ...
     @final
-    def is_(self, other: object) -> bool: ...
+    def is_(self, other: Any) -> bool: ...
     def __len__(self) -> int: ...
     def __array__(
         self, dtype: _str | np.dtype = ..., copy: bool | None = ...
@@ -403,7 +403,7 @@ class Index(IndexOpsMixin[S1], ElementOpsMixin[S1]):
     @property
     def nlevels(self) -> int: ...
     def get_level_values(self, level: int | _str) -> Index: ...
-    def droplevel(self, level: Level | list[Level] = 0): ...
+    def droplevel(self, level: Level | Sequence[Level] = 0) -> Self: ...
     @property
     def is_monotonic_increasing(self) -> bool: ...
     @property
@@ -414,16 +414,13 @@ class Index(IndexOpsMixin[S1], ElementOpsMixin[S1]):
     def has_duplicates(self) -> bool: ...
     @property
     def inferred_type(self) -> _str: ...
-    def __reduce__(self): ...
     @property
     def hasnans(self) -> bool: ...
     @final
-    def isna(self): ...
-    isnull = ...
+    def isna(self) -> Index[bool]: ...
     @final
-    def notna(self): ...
-    notnull = ...
-    def fillna(self, value=...): ...
+    def notna(self) -> Index[bool]: ...
+    def fillna(self, value: Scalar) -> Index: ...
     def dropna(self, how: AnyAll = "any") -> Self: ...
     def unique(self, level: Hashable | None = None) -> Self: ...
     def drop_duplicates(self, *, keep: DropKeep = ...) -> Self: ...
@@ -489,7 +486,7 @@ class Index(IndexOpsMixin[S1], ElementOpsMixin[S1]):
     ) -> Index: ...
     @property
     def values(self) -> np_1darray: ...
-    def memory_usage(self, deep: bool = False): ...
+    def memory_usage(self, deep: bool = False) -> int: ...
     @overload
     def where(
         self,
@@ -503,8 +500,6 @@ class Index(IndexOpsMixin[S1], ElementOpsMixin[S1]):
         other: Scalar | AnyArrayLike | None = None,
     ) -> Index: ...
     def __contains__(self, key: Hashable) -> bool: ...
-    @final
-    def __setitem__(self, key, value) -> None: ...
     @overload
     def __getitem__(
         self,
@@ -519,9 +514,9 @@ class Index(IndexOpsMixin[S1], ElementOpsMixin[S1]):
     @overload
     def append(self, other: Index | Sequence[Index]) -> Index: ...
     def putmask(self, mask, value): ...
-    def equals(self, other: object) -> bool: ...
+    def equals(self, other: Any) -> bool: ...
     @final
-    def identical(self, other) -> bool: ...
+    def identical(self, other: Any) -> bool: ...
     @final
     def asof(self, label): ...
     def asof_locs(self, where, mask): ...
diff --git a/pandas-stubs/core/indexes/multi.pyi b/pandas-stubs/core/indexes/multi.pyi
index 544ff061a..3b3564295 100644
--- a/pandas-stubs/core/indexes/multi.pyi
+++ b/pandas-stubs/core/indexes/multi.pyi
@@ -109,6 +109,7 @@ class MultiIndex(Index):
     def is_monotonic_decreasing(self) -> bool: ...
     def duplicated(self, keep: DropKeep = "first"): ...
     def dropna(self, how: AnyAll = "any") -> Self: ...
+    def droplevel(self, level: Level | Sequence[Level] = 0) -> MultiIndex | Index: ...  # type: ignore[override]
     def get_level_values(self, level: str | int) -> Index: ...
     def unique(self, level=...): ...
     def to_frame(  # type: ignore[override]  # pyright: ignore[reportIncompatibleMethodOverride]
diff --git a/tests/indexes/test_indexes.py b/tests/indexes/test_indexes.py
index 45cd97fc1..5b3d9416a 100644
--- a/tests/indexes/test_indexes.py
+++ b/tests/indexes/test_indexes.py
@@ -1526,7 +1526,6 @@ def test_datetimeindex_where() -> None:
 
 
 def test_index_set_names() -> None:
-    """Test Index.where with multiple types of other GH1419."""
     idx = pd.Index([1, 2])
     check(
         assert_type(idx.set_names("chinchilla"), "pd.Index[int]"), pd.Index, np.integer
@@ -1546,3 +1545,21 @@ def test_index_set_names() -> None:
     )
     mi = cast("pd.MultiIndex", pd.Index([(1,)]))
     check(assert_type(mi.set_names(1), pd.MultiIndex), pd.MultiIndex, tuple)
+
+
+def test_index_droplevel() -> None:
+    idx = pd.Index([1, 2])
+    check(assert_type(idx.droplevel([]), "pd.Index[int]"), pd.Index, np.integer)
+    mi = pd.MultiIndex.from_arrays([[1, 2, 3], [4, 5, 6]], names=["elk", "owl"])
+    check(assert_type(mi.droplevel([]), pd.MultiIndex | pd.Index), pd.MultiIndex)
+    check(assert_type(mi.droplevel([0]), pd.MultiIndex | pd.Index), pd.Index)
+    check(assert_type(mi.droplevel((0,)), pd.MultiIndex | pd.Index), pd.Index)
+    check(assert_type(mi.droplevel(["elk"]), pd.MultiIndex | pd.Index), pd.Index)
+    check(assert_type(mi.droplevel(("elk",)), pd.MultiIndex | pd.Index), pd.Index)
+    check(assert_type(mi.droplevel(0), pd.MultiIndex | pd.Index), pd.Index)
+
+
+def test_index_setitem() -> None:
+    idx = pd.Index([1, 2])
+    if TYPE_CHECKING_INVALID_USAGE:
+        idx[0] = 999  # type: ignore[index]  # pyright: ignore[reportIndexIssue]