diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 7395f9d2dcb9e..d5f85682dba61 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -274,6 +274,7 @@ Groupby/resample/rolling
 - Bug in :meth:`Series.rolling.apply`, :meth:`DataFrame.rolling.apply`, :meth:`Series.expanding.apply` and :meth:`DataFrame.expanding.apply` with ``engine="numba"`` where ``*args`` were being cached with the user passed function (:issue:`42287`)
 - Bug in :meth:`DataFrame.groupby.rolling.var` would calculate the rolling variance only on the first group (:issue:`42442`)
 - Bug in :meth:`GroupBy.shift` that would return the grouping columns if ``fill_value`` was not None (:issue:`41556`)
+- Bug in :meth:`SeriesGroupBy.nlargest` and :meth:`SeriesGroupBy.nsmallest` would have an inconsistent index when the input Series was sorted and ``n`` was greater than or equal to all group sizes (:issue:`15272`, :issue:`16345`, :issue:`29129`)
 - Bug in :meth:`pandas.DataFrame.ewm`, where non-float64 dtypes were silently failing (:issue:`42452`)
 
 Reshaping
diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index 59c57cf4a1ea0..a1c2d57a117c0 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -870,6 +870,24 @@ def pct_change(self, periods=1, fill_method="pad", limit=None, freq=None):
 
         return (filled / shifted) - 1
 
+    @doc(Series.nlargest)
+    def nlargest(self, n: int = 5, keep: str = "first"):
+        f = partial(Series.nlargest, n=n, keep=keep)
+        data = self._obj_with_exclusions
+        # Don't change behavior if result index happens to be the same, i.e.
+        # already ordered and n >= all group sizes.
+        result = self._python_apply_general(f, data, not_indexed_same=True)
+        return result
+
+    @doc(Series.nsmallest)
+    def nsmallest(self, n: int = 5, keep: str = "first"):
+        f = partial(Series.nsmallest, n=n, keep=keep)
+        data = self._obj_with_exclusions
+        # Don't change behavior if result index happens to be the same, i.e.
+        # already ordered and n >= all group sizes.
+        result = self._python_apply_general(f, data, not_indexed_same=True)
+        return result
+
 
 @pin_allowlisted_properties(DataFrame, base.dataframe_apply_allowlist)
 class DataFrameGroupBy(GroupBy[DataFrame]):
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index 5f9b1dec062f8..61f6e669aca53 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -1275,7 +1275,7 @@ def f(g):
 
     @final
     def _python_apply_general(
-        self, f: F, data: DataFrame | Series
+        self, f: F, data: DataFrame | Series, not_indexed_same: bool | None = None
     ) -> DataFrame | Series:
         """
         Apply function f in python space
@@ -1286,6 +1286,10 @@ def _python_apply_general(
             Function to apply
         data : Series or DataFrame
             Data to apply f to
+        not_indexed_same: bool, optional
+            When specified, overrides the value of not_indexed_same. Apply behaves
+            differently when the result index is equal to the input index, but
+            this can be coincidental leading to value-dependent behavior.
 
         Returns
         -------
@@ -1294,8 +1298,11 @@ def _python_apply_general(
         """
         keys, values, mutated = self.grouper.apply(f, data, self.axis)
 
+        if not_indexed_same is None:
+            not_indexed_same = mutated or self.mutated
+
         return self._wrap_applied_output(
-            data, keys, values, not_indexed_same=mutated or self.mutated
+            data, keys, values, not_indexed_same=not_indexed_same
         )
 
     @final
diff --git a/pandas/tests/groupby/test_function.py b/pandas/tests/groupby/test_function.py
index 77e5e9ba133f5..84ec43b5d38d7 100644
--- a/pandas/tests/groupby/test_function.py
+++ b/pandas/tests/groupby/test_function.py
@@ -680,6 +680,23 @@ def test_nsmallest():
     tm.assert_series_equal(gb.nsmallest(3, keep="last"), e)
 
 
+@pytest.mark.parametrize(
+    "data, groups",
+    [([0, 1, 2, 3], [0, 0, 1, 1]), ([0], [0])],
+)
+@pytest.mark.parametrize("method", ["nlargest", "nsmallest"])
+def test_nlargest_and_smallest_noop(data, groups, method):
+    # GH 15272, GH 16345, GH 29129
+    # Test nlargest/smallest when it results in a noop,
+    # i.e. input is sorted and group size <= n
+    if method == "nlargest":
+        data = list(reversed(data))
+    ser = Series(data, name="a")
+    result = getattr(ser.groupby(groups), method)(n=2)
+    expected = Series(data, index=MultiIndex.from_arrays([groups, ser.index]), name="a")
+    tm.assert_series_equal(result, expected)
+
+
 @pytest.mark.parametrize("func", ["cumprod", "cumsum"])
 def test_numpy_compat(func):
     # see gh-12811