diff --git a/doc/source/whatsnew/v0.20.3.txt b/doc/source/whatsnew/v0.20.3.txt
index b2d382a3202a5..409affade712b 100644
--- a/doc/source/whatsnew/v0.20.3.txt
+++ b/doc/source/whatsnew/v0.20.3.txt
@@ -39,7 +39,7 @@ Bug Fixes
 - Fixed issue with dataframe scatter plot for categorical data that reports incorrect column key not found when categorical data is used for plotting (:issue:`16199`)
 - Fixed a pytest marker failing downstream packages' tests suites (:issue:`16680`)
 - Fixed compat with loading a ``DataFrame`` with a ``PeriodIndex``, from a ``format='fixed'`` HDFStore, in Python 3, that was written in Python 2 (:issue:`16781`)
-
+- Fixed a bug in failing to compute rolling computations of a column-MultiIndexed ``DataFrame`` (:issue:`16789`, :issue:`16825`)
 
 Conversion
 ^^^^^^^^^^
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index f30da5b05f8ae..38ae91f10e249 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -1388,6 +1388,9 @@ def __getitem__(self, key):
                 # cannot be sure whether the result will be sorted
                 sortorder = None
 
+                if isinstance(key, Index):
+                    key = np.asarray(key)
+
             new_labels = [lab[key] for lab in self.labels]
 
             return MultiIndex(levels=self.levels, labels=new_labels,
diff --git a/pandas/core/window.py b/pandas/core/window.py
index ba7e79944ab0e..b717b794b147b 100644
--- a/pandas/core/window.py
+++ b/pandas/core/window.py
@@ -831,7 +831,7 @@ def count(self):
 
         return self._wrap_results(results, blocks, obj)
 
-    _shared_docs['apply'] = dedent("""
+    _shared_docs['apply'] = dedent(r"""
     %(name)s function apply
 
     Parameters
@@ -1911,7 +1911,8 @@ def dataframe_from_int_dict(data, frame_template):
 
                 # TODO: not the most efficient (perf-wise)
                 # though not bad code-wise
-                from pandas import Panel, MultiIndex, Index
+                from pandas import Panel, MultiIndex
+
                 with warnings.catch_warnings(record=True):
                     p = Panel.from_dict(results).swapaxes('items', 'major')
                     if len(p.major_axis) > 0:
@@ -1934,8 +1935,8 @@ def dataframe_from_int_dict(data, frame_template):
                 # reset our index names to arg1 names
                 # reset our column names to arg2 names
                 # careful not to mutate the original names
-                result.columns = Index(result.columns).set_names(
-                    arg2.columns.name)
+                result.columns = result.columns.set_names(
+                    arg2.columns.names)
                 result.index = result.index.set_names(
                     [arg1.index.name, arg1.columns.name])
 
diff --git a/pandas/tests/test_window.py b/pandas/tests/test_window.py
index cbb3c345a9353..9c3765ffdb716 100644
--- a/pandas/tests/test_window.py
+++ b/pandas/tests/test_window.py
@@ -455,6 +455,17 @@ def tests_empty_df_rolling(self, roller):
         result = DataFrame(index=pd.DatetimeIndex([])).rolling(roller).sum()
         tm.assert_frame_equal(result, expected)
 
+    def test_multi_index_names(self):
+
+        # GH 16789, 16825
+        cols = pd.MultiIndex.from_product([['A', 'B'], ['C', 'D', 'E']],
+                                          names=['1', '2'])
+        df = pd.DataFrame(np.ones((10, 6)), columns=cols)
+        result = df.rolling(3).cov()
+
+        tm.assert_index_equal(result.columns, df.columns)
+        assert result.index.names == [None, '1', '2']
+
 
 class TestExpanding(Base):
 
@@ -501,9 +512,10 @@ def test_numpy_compat(self):
         'expander',
         [1, pytest.mark.xfail(
             reason='GH 16425 expanding with offset not supported')('1s')])
-    def tests_empty_df_expanding(self, expander):
+    def test_empty_df_expanding(self, expander):
         # GH 15819 Verifies that datetime and integer expanding windows can be
         # applied to empty DataFrames
+
         expected = DataFrame()
         result = DataFrame().expanding(expander).sum()
         tm.assert_frame_equal(result, expected)