diff --git a/sklearn/utils/fixes.py b/sklearn/utils/fixes.py
index e0f10bcae8e4e..3f9d2317538de 100644
--- a/sklearn/utils/fixes.py
+++ b/sklearn/utils/fixes.py
@@ -103,7 +103,7 @@ def divide(x1, x2, out=None, dtype=None):
 except TypeError:
     # Compat where astype accepted no copy argument
     def astype(array, dtype, copy=True):
-        if array.dtype == dtype:
+        if not copy and array.dtype == dtype:
             return array
         return array.astype(dtype)
 else:
diff --git a/sklearn/utils/tests/test_fixes.py b/sklearn/utils/tests/test_fixes.py
index 3580aa6acbff7..4494f87b5feb4 100644
--- a/sklearn/utils/tests/test_fixes.py
+++ b/sklearn/utils/tests/test_fixes.py
@@ -6,10 +6,13 @@
 import numpy as np
 
 from nose.tools import assert_equal
+from nose.tools import assert_false
+from nose.tools import assert_true
 from numpy.testing import (assert_almost_equal,
                            assert_array_almost_equal)
 
 from sklearn.utils.fixes import divide, expit
+from sklearn.utils.fixes import astype
 
 
 def test_expit():
@@ -28,3 +31,25 @@ def test_expit():
 
 def test_divide():
     assert_equal(divide(.6, 1), .600000000000)
+
+
+def test_astype_copy_memory():
+    a_int32 = np.ones(3, np.int32)
+
+    # Check that dtype conversion works
+    b_float32 = astype(a_int32, dtype=np.float32, copy=False)
+    assert_equal(b_float32.dtype, np.float32)
+
+    # Changing dtype forces a copy even if copy=False
+    assert_false(np.may_share_memory(b_float32, a_int32))
+
+    # Check that copy can be skipped if requested dtype match
+    c_int32 = astype(a_int32, dtype=np.int32, copy=False)
+    assert_true(c_int32 is a_int32)
+
+    # Check that copy can be forced, and is the case by default:
+    d_int32 = astype(a_int32, dtype=np.int32, copy=True)
+    assert_false(np.may_share_memory(d_int32, a_int32))
+
+    e_int32 = astype(a_int32, dtype=np.int32)
+    assert_false(np.may_share_memory(e_int32, a_int32))