diff --git a/pandas/core/series.py b/pandas/core/series.py
index 7abd95c68ea2b..1ef6f2d7eee22 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -41,7 +41,11 @@
     maybe_cast_to_datetime, maybe_castable,
     construct_1d_arraylike_from_scalar,
     construct_1d_object_array_from_listlike)
-from pandas.core.dtypes.missing import isna, notna, remove_na_arraylike
+from pandas.core.dtypes.missing import (
+    isna,
+    notna,
+    remove_na_arraylike,
+    na_value_for_dtype)
 
 from pandas.core.index import (Index, MultiIndex, InvalidIndexError,
                                Float64Index, _ensure_index)
@@ -300,6 +304,11 @@ def _init_dict(self, data, index=None, dtype=None):
         if data:
             keys, values = zip(*compat.iteritems(data))
             values = list(values)
+        elif index is not None:
+            # fastpath for Series(data=None). Just use broadcasting a scalar
+            # instead of reindexing.
+            values = na_value_for_dtype(dtype)
+            keys = index
         else:
             keys, values = [], []
 
@@ -307,9 +316,11 @@ def _init_dict(self, data, index=None, dtype=None):
         s = Series(values, index=keys, dtype=dtype)
 
         # Now we just make sure the order is respected, if any
-        if index is not None:
+        if data and index is not None:
             s = s.reindex(index, copy=False)
-        elif not PY36 and not isinstance(data, OrderedDict):
+        elif not PY36 and not isinstance(data, OrderedDict) and data:
+            # Need the `and data` to avoid sorting Series(None, index=[...])
+            # since that isn't really dict-like
             try:
                 s = s.sort_index()
             except TypeError:
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index 82b5b1c10fa2d..7e59325c32ddc 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -122,6 +122,21 @@ def test_constructor_nan(self, input_arg):
 
         assert_series_equal(empty, empty2, check_index_type=False)
 
+    @pytest.mark.parametrize('dtype', [
+        'f8', 'i8', 'M8[ns]', 'm8[ns]', 'category', 'object',
+        'datetime64[ns, UTC]',
+    ])
+    @pytest.mark.parametrize('index', [None, pd.Index([])])
+    def test_constructor_dtype_only(self, dtype, index):
+        # GH-20865
+        result = pd.Series(dtype=dtype, index=index)
+        assert result.dtype == dtype
+        assert len(result) == 0
+
+    def test_constructor_no_data_index_order(self):
+        result = pd.Series(index=['b', 'a', 'c'])
+        assert result.index.tolist() == ['b', 'a', 'c']
+
     def test_constructor_series(self):
         index1 = ['d', 'b', 'a', 'c']
         index2 = sorted(index1)