diff --git a/xarray/core/rolling.py b/xarray/core/rolling.py
index ad9b17fef92..399e057d915 100644
--- a/xarray/core/rolling.py
+++ b/xarray/core/rolling.py
@@ -194,7 +194,7 @@ def construct(self, window_dim, stride=1, fill_value=dtypes.NA):
                            coords=self.obj.coords)
         return result.isel(**{self.dim: slice(None, None, stride)})
 
-    def reduce(self, func, **kwargs):
+    def reduce(self, func, include_border=False, **kwargs):
         """Reduce the items in this group by applying `func` along some
         dimension(s).
 
@@ -204,6 +204,9 @@ def reduce(self, func, **kwargs):
             Function which can be called in the form
             `func(x, **kwargs)` to return the result of collapsing an
             np.ndarray over an the rolling dimension.
+        include_border : boolean, False
+            Include results where the rolling window partially falls outside
+            of the array border.  If False, these locations contain np.nan.
         **kwargs : dict
             Additional keyword arguments passed on to `func`.
 
@@ -211,11 +214,36 @@ def reduce(self, func, **kwargs):
         -------
         reduced : DataArray
             Array with summarized data.
+
+        Examples
+        --------
+        >>> da = DataArray(np.arange(8).reshape(2, 4), dims=('a', 'b'))
+        >>>
+        >>> rolling = da.rolling(b=3)
+        >>> rolling.construct('window_dim')
+        <xarray.DataArray (a: 2, b: 4, window_dim: 3)>
+        array([[[np.nan, np.nan, 0], [np.nan, 0, 1], [0, 1, 2], [1, 2, 3]],
+               [[np.nan, np.nan, 4], [np.nan, 4, 5], [4, 5, 6], [5, 6, 7]]])
+        Dimensions without coordinates: a, b, window_dim
+        >>>
+        >>> rolling.reduce(np.sum)
+        <xarray.DataArray (a: 2, b: 4)>
+        array([[nan, nan,  3.,  6.],
+               [nan, nan, 15., 18.]])
+        Dimensions without coordinates: a, b
+        >>>
+        >>> rolling.reduce(np.nansum, include_border=True)
+        <xarray.DataArray (a: 2, b: 4)>
+        array([[ 0.,  1.,  3.,  6.],
+               [ 4.,  9., 15., 18.]])
         """
         rolling_dim = utils.get_temp_dimname(self.obj.dims, '_rolling_dim')
         windows = self.construct(rolling_dim)
         result = windows.reduce(func, dim=rolling_dim, **kwargs)
 
+        if include_border:
+            return result
+
         # Find valid windows based on count.
         counts = self._counts()
         return result.where(counts >= self._min_periods)
@@ -347,7 +375,7 @@ def __init__(self, obj, windows, min_periods=None, center=False):
                 self.rollings[key] = DataArrayRolling(
                     da, windows, min_periods, center)
 
-    def reduce(self, func, **kwargs):
+    def reduce(self, func, include_border=False, **kwargs):
         """Reduce the items in this group by applying `func` along some
         dimension(s).
 
@@ -357,6 +385,9 @@ def reduce(self, func, **kwargs):
             Function which can be called in the form
             `func(x, **kwargs)` to return the result of collapsing an
             np.ndarray over an the rolling dimension.
+        include_border : boolean, False
+            Include results where the rolling window partially falls outside
+            of the array border.  If False, these locations contain np.nan.
         **kwargs : dict
             Additional keyword arguments passed on to `func`.
 
@@ -369,7 +400,8 @@ def reduce(self, func, **kwargs):
         reduced = OrderedDict()
         for key, da in self.obj.data_vars.items():
             if self.dim in da.dims:
-                reduced[key] = self.rollings[key].reduce(func, **kwargs)
+                reduced[key] = self.rollings[key].reduce(
+                    func, include_border=include_border, **kwargs)
             else:
                 reduced[key] = self.obj[key]
         return Dataset(reduced, coords=self.obj.coords)