diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 26b9a880dd2c7..76fbb9884753d 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -3161,6 +3161,14 @@ def copy(self, deep=True):
         data = self._data.copy(deep=deep)
         return self._constructor(data).__finalize__(self)
 
+    def __copy__(self, deep=True):
+        return self.copy(deep=deep)
+
+    def __deepcopy__(self, memo=None):
+        if memo is None:
+            memo = {}
+        return self.copy(deep=True)
+
     def _convert(self, datetime=False, numeric=False, timedelta=False,
                  coerce=False, copy=True):
         """
diff --git a/pandas/indexes/base.py b/pandas/indexes/base.py
index e51824e72a2a0..f1f37622b2a74 100644
--- a/pandas/indexes/base.py
+++ b/pandas/indexes/base.py
@@ -724,7 +724,13 @@ def copy(self, name=None, deep=False, dtype=None, **kwargs):
             new_index = new_index.astype(dtype)
         return new_index
 
-    __copy__ = copy
+    def __copy__(self, **kwargs):
+        return self.copy(**kwargs)
+
+    def __deepcopy__(self, memo=None):
+        if memo is None:
+            memo = {}
+        return self.copy(deep=True)
 
     def _validate_names(self, name=None, names=None, deep=False):
         """
@@ -1480,11 +1486,6 @@ def __setstate__(self, state):
 
     _unpickle_compat = __setstate__
 
-    def __deepcopy__(self, memo=None):
-        if memo is None:
-            memo = {}
-        return self.copy(deep=True)
-
     def __nonzero__(self):
         raise ValueError("The truth value of a {0} is ambiguous. "
                          "Use a.empty, a.bool(), a.item(), a.any() or a.all()."
diff --git a/pandas/tests/test_generic.py b/pandas/tests/test_generic.py
index b087ca21d3c25..9ad8b5da7eea8 100644
--- a/pandas/tests/test_generic.py
+++ b/pandas/tests/test_generic.py
@@ -2,6 +2,7 @@
 # pylint: disable-msg=E1101,W0612
 
 from operator import methodcaller
+from copy import copy, deepcopy
 import pytest
 import numpy as np
 from numpy import nan
@@ -675,6 +676,17 @@ def test_validate_bool_args(self):
             with self.assertRaises(ValueError):
                 super(DataFrame, df).mask(cond=df.a > 2, inplace=value)
 
+    def test_copy_and_deepcopy(self):
+        for shape in [0, 1, 2]:
+            obj = self._construct(shape)
+            for func in [copy,
+                         deepcopy,
+                         lambda x: x.copy(deep=False),
+                         lambda x: x.copy(deep=True)]:
+                obj_copy = func(obj)
+                self.assertIsNot(obj_copy, obj)
+                self._compare(obj_copy, obj)
+
 
 class TestSeries(tm.TestCase, Generic):
     _typ = Series
@@ -1539,6 +1551,14 @@ def test_to_xarray(self):
                            expected,
                            check_index_type=False)
 
+    def test_deepcopy_empty(self):
+        # This test covers empty frame copying with non-empty column sets
+        # as reported in issue GH15370
+        empty_frame = DataFrame(data=[], index=[], columns=['A'])
+        empty_frame_copy = deepcopy(empty_frame)
+
+        self._compare(empty_frame_copy, empty_frame)
+
 
 class TestPanel(tm.TestCase, Generic):
     _typ = Panel
@@ -1569,6 +1589,9 @@ class TestPanel4D(tm.TestCase, Generic):
     def test_sample(self):
         pytest.skip("sample on Panel4D")
 
+    def test_copy_and_deepcopy(self):
+        pytest.skip("copy_and_deepcopy on Panel4D")
+
     def test_to_xarray(self):
 
         tm._skip_if_no_xarray()