diff -r 3156dd82df2d Lib/test/test_os.py
--- a/Lib/test/test_os.py	Wed Jun 10 15:44:18 2015 -0700
+++ b/Lib/test/test_os.py	Fri Jun 12 00:51:26 2015 +0200
@@ -418,19 +418,27 @@ class StatAttributeTests(unittest.TestCa
         self._test_utime(self.fname, getattr, utime, 10)
         self._test_utime(support.TESTFN, getattr, utime, 10)
 
-
-    def _test_utime_ns(self, set_times_ns, test_dir=True):
-        def getattr_ns(o, attr):
-            return getattr(o, attr + "_ns")
-        ten_s = 10 * 1000 * 1000 * 1000
-        self._test_utime(self.fname, getattr_ns, set_times_ns, ten_s)
-        if test_dir:
-            self._test_utime(support.TESTFN, getattr_ns, set_times_ns, ten_s)
+    def _test_utime_ns(self, utime):
+        # Use positive timestamps with a resolution of 1 microsecond smaller
+        # than 2^24 seconds to avoid rounding issues.
+        #
+        # The C internal function used by os.utime() may only support a
+        # resolution of 1 us, so use a timestamp of 1 us. Writing a portable
+        # test with a resolution of 1 ns requires more work: see the issue
+        # #15745.
+        atime_ns = 1002003000   # 1.002003 seconds
+        mtime_ns = 4005006000   # 4.005006 seconds
+        utime(self.fname, atime_ns, mtime_ns)
+        st = os.stat(self.fname)
+        self.assertEqual(st.st_atime_ns, atime_ns)
+        self.assertEqual(st.st_mtime_ns, mtime_ns)
 
     def test_utime_ns(self):
-        def utime_ns(file, times):
-            return os.utime(file, ns=times)
-        self._test_utime_ns(utime_ns)
+        def utime(filename, atime_ns, mtime_ns):
+            # test utimensat(timespec), utimes(timeval), utime(utimbuf)
+            # or utime(time_t)
+            os.utime(filename, ns=(atime_ns, mtime_ns))
+        self._test_utime_ns(utime)
 
     requires_utime_dir_fd = unittest.skipUnless(
                                 os.utime in os.supports_dir_fd,
@@ -443,17 +451,22 @@ class StatAttributeTests(unittest.TestCa
                                 "follow_symlinks support for utime required for this test.")
 
     @requires_utime_nofollow_symlinks
-    def test_lutimes_ns(self):
-        def lutimes_ns(file, times):
-            return os.utime(file, ns=times, follow_symlinks=False)
-        self._test_utime_ns(lutimes_ns)
+    def test_utime_nofollow_symlinks(self):
+        def utime(filename, atime_ns, mtime_ns):
+            # use follow_symlinks=False to test utimensat(timespec)
+            # or lutimes(timeval)
+            os.utime(filename, ns=(atime_ns, mtime_ns),
+                     follow_symlinks=False)
+        self._test_utime_ns(utime)
 
     @requires_utime_fd
     def test_futimes_ns(self):
-        def futimes_ns(file, times):
-            with open(file, "wb") as f:
-                os.utime(f.fileno(), ns=times)
-        self._test_utime_ns(futimes_ns, test_dir=False)
+        def utime(filename, atime_ns, mtime_ns):
+            with open(filename, 'wb') as fp:
+                # use a file descriptor to test futimens(timespec)
+                # or futimes(timeval)
+                os.utime(fp.fileno(), ns=(atime_ns, mtime_ns))
+        self._test_utime_ns(utime)
 
     def _utime_invalid_arguments(self, name, arg):
         with self.assertRaises(ValueError):