diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 3cb2b7c1b72720..9c3c11b808b37e 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -2967,11 +2967,11 @@ def rename(self, mapper=None, index=None, columns=None, axis=None,
 
         Parameters
         ----------
-        mapper : dict-like or function, optional
-            Applied to the axis specified by ``axis``
-        index, columns : scalar, list-like, dict-like or function, optional
+        mapper, index, columns : dict-like or function, optional
             dict-like or functions transformations to apply to
-            that axis' values
+            that axis' values. Use either ``mapper`` and ``axis`` to
+            specify the axis to target with ``mapper``, or ``index`` and
+            ``columns``.
         axis : int or str, optional
             Axis to target with ``mapper``. Can be either the axis name
             ('index', 'columns') or number (0, 1). The default is 'index'.
@@ -2990,7 +2990,7 @@ def rename(self, mapper=None, index=None, columns=None, axis=None,
 
         See Also
         --------
-        pandas.NDFrame.rename_axis
+        pandas.DataFrame.rename_axis
 
         Examples
         --------
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 0a9eb77f199a7c..8f495e38105a08 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -2526,7 +2526,7 @@ def align(self, other, join='outer', axis=None, level=None, copy=True,
                                          broadcast_axis=broadcast_axis)
 
     def rename(self, index=None, **kwargs):
-        """Alter Series row labels or name
+        """Alter Series index labels or name
 
         Function / dict values must be unique (1-to-1). Labels not contained in
         a dict / Series will be left as-is. Extra labels listed don't throw an
@@ -2538,10 +2538,11 @@ def rename(self, index=None, **kwargs):
 
         Parameters
         ----------
-        index : scalar, list-like, dict-like or function, optional
+        index : scalar, hashable sequence, dict-like or function, optional
             dict-like or functions are transformations to apply to
             the index.
-            Scalar or list-like will alter the ``Series.name`` attribute.
+            Scalar or hashable sequence-like will alter the ``Series.name``
+            attribute.
         copy : boolean, default True
             Also copy underlying data
         inplace : boolean, default False
@@ -2557,7 +2558,7 @@ def rename(self, index=None, **kwargs):
 
         See Also
         --------
-        pandas.DataFrame.rename_axis
+        pandas.Series.rename_axis
 
         Examples
         --------