diff --git a/dask/dataframe/core.py b/dask/dataframe/core.py
index bc9ba5e142e..c7ac85014a7 100644
--- a/dask/dataframe/core.py
+++ b/dask/dataframe/core.py
@@ -1410,10 +1410,34 @@ def dtypes(self):
             self._pd, self._known_dtype = self._build_pd(self.head())
             return self._pd.dtypes
 
-    @derived_from(pd.DataFrame)
-    def set_index(self, other, drop=True, **kwargs):
-        from .shuffle import set_index
-        return set_index(self, other, drop=drop, **kwargs)
+    def set_index(self, other, drop=True, sorted=False, **kwargs):
+        """ Set the DataFrame index 9row labels) using an existing column
+
+        This operation in dask.dataframe is expensive.  If the input column is
+        sorted then we accomplish the set_index in a single full read of that
+        column.  However, if the input column is not sorted then this operation
+        triggers a full shuffle, which can take a while and only works on a
+        single machine (not distributed).
+
+        Parameters
+        ----------
+        other: Series or label
+        drop: boolean, default True
+            Delete columns to be used as the new index
+        sorted: boolean, default False
+            Set to True if the new index column is already sorted
+
+        Examples
+        --------
+        >>> df.set_index('x')  # doctest: +SKIP
+        >>> df.set_index(d.x)  # doctest: +SKIP
+        >>> df.set_index(d.timestamp, sorted=True)  # doctest: +SKIP
+        """
+        if sorted:
+            return set_sorted_index(self, other, drop=drop, **kwargs)
+        else:
+            from .shuffle import set_index
+            return set_index(self, other, drop=drop, **kwargs)
 
     def set_partition(self, column, divisions, **kwargs):
         """ Set explicit divisions for new column index
@@ -2061,9 +2085,9 @@ def map_partitions(func, metadata, *args, **kwargs):
     metadata = _extract_pd(metadata)
 
     assert callable(func)
-    token = kwargs.pop('token', 'map-partitions')
+    token = kwargs.pop('token', None)
     token_key = tokenize(token or func, metadata, kwargs, *args)
-    name = '{0}-{1}'.format(token, token_key)
+    name = '{0}-{1}'.format(token or 'map-partitions', token_key)
 
     if all(isinstance(arg, Scalar) for arg in args):
         dask = {(name, 0):
@@ -2646,3 +2670,32 @@ def try_loc(df, ind):
         return df.loc[ind]
     except KeyError:
         return df.head(0)
+
+
+def set_sorted_index(df, index, drop=True, **kwargs):
+    if not isinstance(index, Series):
+        index2 = df[index]
+        meta = df._pd.set_index(index, drop=drop)
+    else:
+        index2 = index
+        meta = df._pd.set_index(index._pd, drop=drop)
+
+    mins = index2.map_partitions(pd.Series.min)
+    maxes = index2.map_partitions(pd.Series.max)
+    mins, maxes = compute(mins, maxes, **kwargs)
+
+    if (sorted(mins) != list(mins) or
+        sorted(maxes) != list(maxes) or
+        any(a >= b for a, b in zip(mins, maxes))):
+        raise ValueError("Column not properly sorted", mins, maxes)
+
+    divisions = tuple(mins) + (list(maxes)[-1],)
+
+    result = map_partitions(_set_sorted_index, meta, df, index, drop=drop)
+    result.divisions = divisions
+
+    return result
+
+
+def _set_sorted_index(df, idx, drop):
+    return df.set_index(idx, drop=drop)
diff --git a/dask/dataframe/tests/test_dataframe.py b/dask/dataframe/tests/test_dataframe.py
index 8d3498a2a61..ce00b6f4c76 100644
--- a/dask/dataframe/tests/test_dataframe.py
+++ b/dask/dataframe/tests/test_dataframe.py
@@ -1685,3 +1685,33 @@ def iseven(x):
               b.groupby(iseven).y.sum())
     assert eq(a.y.groupby(iseven).sum(),
               b.y.groupby(iseven).sum())
+
+
+def test_set_index_sorted_true():
+    df = pd.DataFrame({'x': [1, 2, 3, 4],
+                       'y': [10, 20, 30, 40],
+                       'z': [4, 3, 2, 1]})
+    a = dd.from_pandas(df, 2, sort=False)
+    assert not a.known_divisions
+
+    b = a.set_index('x', sorted=True)
+    assert b.known_divisions
+    assert set(a.dask).issubset(set(b.dask))
+
+    for drop in [True, False]:
+        eq(a.set_index('x', drop=drop),
+           df.set_index('x', drop=drop))
+        eq(a.set_index(a.x, sorted=True, drop=drop),
+           df.set_index(df.x, drop=drop))
+        eq(a.set_index(a.x + 1, sorted=True, drop=drop),
+           df.set_index(df.x + 1, drop=drop))
+
+    with pytest.raises(ValueError):
+        a.set_index(a.z, sorted=True)
+
+
+def test_methods_tokenize_differently():
+    df = pd.DataFrame({'x': [1, 2, 3, 4]})
+    df = dd.from_pandas(df, npartitions=1)
+    assert (df.x.map_partitions(pd.Series.min)._name !=
+            df.x.map_partitions(pd.Series.max)._name)