diff --git a/doc/source/whatsnew/v0.19.0.txt b/doc/source/whatsnew/v0.19.0.txt
index cc3cc631b9575..0a6095b8076f9 100644
--- a/doc/source/whatsnew/v0.19.0.txt
+++ b/doc/source/whatsnew/v0.19.0.txt
@@ -814,6 +814,9 @@ Note that the limitation is applied to ``fill_value`` which default is ``np.nan`
 - Bug in ``SparseSeries.abs`` incorrectly keeps negative ``fill_value`` (:issue:`13853`)
 - Bug in single row slicing on multi-type ``SparseDataFrame``s, types were previously forced to float (:issue:`13917`)
 - Bug in sparse indexing using ``SparseArray`` with ``bool`` dtype may return incorrect result  (:issue:`13985`)
+- Bug in ``SparseArray`` created from ``SparseSeries`` may lose ``dtype`` (:issue:`13999`)
+- Bug in ``SparseSeries`` comparison with dense returns normal ``Series`` rather than ``SparseSeries`` (:issue:`13999`)
+
 
 .. _whatsnew_0190.indexer_dtype:
 
diff --git a/pandas/sparse/array.py b/pandas/sparse/array.py
index 8d564d0abbf3f..74d592c32d3aa 100644
--- a/pandas/sparse/array.py
+++ b/pandas/sparse/array.py
@@ -188,9 +188,17 @@ def __new__(cls, data, sparse_index=None, index=None, kind='integer',
             values.fill(data)
             data = values
 
+        if isinstance(data, ABCSparseSeries):
+            data = data.values
+        is_sparse_array = isinstance(data, SparseArray)
+
         if dtype is not None:
             dtype = np.dtype(dtype)
-        is_sparse_array = isinstance(data, SparseArray)
+        if is_sparse_array:
+            # temp, always inherit passed SparseArray dtype
+            # can be removed after GH 13849
+            dtype = data.dtype
+
         if fill_value is None:
             if is_sparse_array:
                 fill_value = data.fill_value
@@ -211,7 +219,6 @@ def __new__(cls, data, sparse_index=None, index=None, kind='integer',
                     raise AssertionError("Non array-like type {0} must have"
                                          " the same length as the"
                                          " index".format(type(values)))
-
         # Create array, do *not* copy data by default
         if copy:
             try:
diff --git a/pandas/sparse/series.py b/pandas/sparse/series.py
index 4ad77b4deab4f..94834ac22166b 100644
--- a/pandas/sparse/series.py
+++ b/pandas/sparse/series.py
@@ -806,7 +806,7 @@ def from_coo(cls, A, dense_index=False):
 # overwrite basic arithmetic to use SparseSeries version
 # force methods to overwrite previous definitions.
 ops.add_special_arithmetic_methods(SparseSeries, _arith_method,
-                                   comp_method=None,
+                                   comp_method=_arith_method,
                                    bool_method=None, use_numexpr=False,
                                    force=True)
 
diff --git a/pandas/sparse/tests/test_arithmetics.py b/pandas/sparse/tests/test_arithmetics.py
index ec8bc4d8634e6..ab84308e02e7c 100644
--- a/pandas/sparse/tests/test_arithmetics.py
+++ b/pandas/sparse/tests/test_arithmetics.py
@@ -358,11 +358,6 @@ class TestSparseSeriesArithmetic(TestSparseArrayArithmetics):
     def _assert(self, a, b):
         tm.assert_series_equal(a, b)
 
-    def _check_bool_result(self, res):
-        # ToDo: Must return SparseSeries after GH 667
-        tm.assertIsInstance(res, self._base)
-        self.assertEqual(res.dtype, np.bool)
-
     def test_alignment(self):
         da = pd.Series(np.arange(4))
         db = pd.Series(np.arange(4), index=[1, 2, 3, 4])
diff --git a/pandas/sparse/tests/test_array.py b/pandas/sparse/tests/test_array.py
index 70cda5acc3f4c..e702b7ed5e349 100644
--- a/pandas/sparse/tests/test_array.py
+++ b/pandas/sparse/tests/test_array.py
@@ -7,7 +7,7 @@
 import numpy as np
 
 from pandas import _np_version_under1p8
-from pandas.sparse.api import SparseArray
+from pandas.sparse.api import SparseArray, SparseSeries
 from pandas._sparse import IntIndex
 from pandas.util.testing import assert_almost_equal, assertRaisesRegexp
 import pandas.util.testing as tm
@@ -102,6 +102,32 @@ def test_constructor_spindex_dtype(self):
         self.assertEqual(arr.dtype, np.int64)
         self.assertEqual(arr.fill_value, 0)
 
+    def test_sparseseries_roundtrip(self):
+        # GH 13999
+        for kind in ['integer', 'block']:
+            for fill in [1, np.nan, 0]:
+                arr = SparseArray([np.nan, 1, np.nan, 2, 3], kind=kind,
+                                  fill_value=fill)
+                res = SparseArray(SparseSeries(arr))
+                tm.assert_sp_array_equal(arr, res)
+
+                arr = SparseArray([0, 0, 0, 1, 1, 2], dtype=np.int64,
+                                  kind=kind, fill_value=fill)
+                res = SparseArray(SparseSeries(arr), dtype=np.int64)
+                tm.assert_sp_array_equal(arr, res)
+
+                res = SparseArray(SparseSeries(arr))
+                tm.assert_sp_array_equal(arr, res)
+
+            for fill in [True, False, np.nan]:
+                arr = SparseArray([True, False, True, True], dtype=np.bool,
+                                  kind=kind, fill_value=fill)
+                res = SparseArray(SparseSeries(arr))
+                tm.assert_sp_array_equal(arr, res)
+
+                res = SparseArray(SparseSeries(arr))
+                tm.assert_sp_array_equal(arr, res)
+
     def test_get_item(self):
 
         self.assertTrue(np.isnan(self.arr[1]))