diff --git a/Lib/fileinput.py b/Lib/fileinput.py
index 11ba82d..de29518 100644
--- a/Lib/fileinput.py
+++ b/Lib/fileinput.py
@@ -224,7 +224,7 @@
                              "'r', 'rU', 'U' and 'rb'")
         if 'U' in mode:
             import warnings
-            warnings.warn("Use of 'U' mode is deprecated",
+            warnings.warn("'U' mode is deprecated",
                           DeprecationWarning, 2)
         self._mode = mode
         if openhook:
diff --git a/Lib/test/test_codecs.py b/Lib/test/test_codecs.py
index 639ce9f..f682380 100644
--- a/Lib/test/test_codecs.py
+++ b/Lib/test/test_codecs.py
@@ -602,7 +602,9 @@
         self.addCleanup(support.unlink, support.TESTFN)
         with open(support.TESTFN, 'wb') as fp:
             fp.write(s)
-        with codecs.open(support.TESTFN, 'U', encoding=self.encoding) as reader:
+        with support.check_warnings(('', DeprecationWarning)):
+            reader = codecs.open(support.TESTFN, 'U', encoding=self.encoding)
+        with reader:
             self.assertEqual(reader.read(), s1)
 
 class UTF16LETest(ReadTest, unittest.TestCase):
diff --git a/Lib/test/test_fileinput.py b/Lib/test/test_fileinput.py
index c5e57d4..db6082c 100644
--- a/Lib/test/test_fileinput.py
+++ b/Lib/test/test_fileinput.py
@@ -22,7 +22,7 @@
 from io import StringIO
 from fileinput import FileInput, hook_encoded
 
-from test.support import verbose, TESTFN, run_unittest
+from test.support import verbose, TESTFN, run_unittest, check_warnings
 from test.support import unlink as safe_unlink
 
 
@@ -224,8 +224,10 @@
         try:
             # try opening in universal newline mode
             t1 = writeTmp(1, [b"A\nB\r\nC\rD"], mode="wb")
-            fi = FileInput(files=t1, mode="U")
-            lines = list(fi)
+            with check_warnings(('', DeprecationWarning)):
+                fi = FileInput(files=t1, mode="U")
+            with check_warnings(('', DeprecationWarning)):
+                lines = list(fi)
             self.assertEqual(lines, ["A\n", "B\n", "C\n", "D"])
         finally:
             remove_tempfiles(t1)
diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
index c1ea6f2..57f3659 100644
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -2777,7 +2777,8 @@
         self.assertEqual(f.mode, "wb")
         f.close()
 
-        f = self.open(support.TESTFN, "U")
+        with support.check_warnings(('', DeprecationWarning)):
+            f = self.open(support.TESTFN, "U")
         self.assertEqual(f.name,            support.TESTFN)
         self.assertEqual(f.buffer.name,     support.TESTFN)
         self.assertEqual(f.buffer.raw.name, support.TESTFN)
diff --git a/Lib/test/test_zipfile.py b/Lib/test/test_zipfile.py
index c15ea9f..49eccbb 100644
--- a/Lib/test/test_zipfile.py
+++ b/Lib/test/test_zipfile.py
@@ -14,7 +14,7 @@
 
 from test.support import (TESTFN, findfile, unlink,
                           requires_zlib, requires_bz2, requires_lzma,
-                          captured_stdout)
+                          captured_stdout, check_warnings)
 
 TESTFN2 = TESTFN + "2"
 TESTFNDIR = TESTFN + "d"
@@ -35,6 +35,10 @@
         yield f
         test.assertFalse(f.closed)
 
+def openU(zipfp, fn):
+    with check_warnings(('', DeprecationWarning)):
+        return zipfp.open(fn, 'rU')
+
 class AbstractTestsWithSourceFile:
     @classmethod
     def setUpClass(cls):
@@ -875,6 +879,17 @@
                 data += zipfp.read(info)
             self.assertIn(data, {b"foobar", b"barfoo"})
 
+    def test_universal_deprecation(self):
+        f = io.BytesIO()
+        with zipfile.ZipFile(f, "w") as zipfp:
+            zipfp.writestr('spam.txt', b'ababagalamaga')
+
+        with zipfile.ZipFile(f, "r") as zipfp:
+            for mode in 'U', 'rU':
+                with self.assertWarns(DeprecationWarning):
+                    zipopen = zipfp.open('spam.txt', mode)
+                zipopen.close()
+
     def test_universal_readaheads(self):
         f = io.BytesIO()
 
@@ -884,7 +899,7 @@
 
         data2 = b''
         with zipfile.ZipFile(f, 'r') as zipfp, \
-             zipfp.open(TESTFN, 'rU') as zipopen:
+             openU(zipfp, TESTFN) as zipopen:
             for line in zipopen:
                 data2 += line
 
@@ -1613,7 +1628,7 @@
         # Read the ZIP archive
         with zipfile.ZipFile(f, "r") as zipfp:
             for sep, fn in self.arcfiles.items():
-                with zipfp.open(fn, "rU") as fp:
+                with openU(zipfp, fn) as fp:
                     zipdata = fp.read()
                 self.assertEqual(self.arcdata[sep], zipdata)
 
@@ -1627,7 +1642,7 @@
         # Read the ZIP archive
         with zipfile.ZipFile(f, "r") as zipfp:
             for sep, fn in self.arcfiles.items():
-                with zipfp.open(fn, "rU") as zipopen:
+                with openU(zipfp, fn) as zipopen:
                     data = b''
                     while True:
                         read = zipopen.readline()
@@ -1652,7 +1667,7 @@
         # Read the ZIP archive
         with zipfile.ZipFile(f, "r") as zipfp:
             for sep, fn in self.arcfiles.items():
-                with zipfp.open(fn, "rU") as zipopen:
+                with openU(zipfp, fn) as zipopen:
                     for line in self.line_gen:
                         linedata = zipopen.readline()
                         self.assertEqual(linedata, line + b'\n')
@@ -1667,7 +1682,7 @@
         # Read the ZIP archive
         with zipfile.ZipFile(f, "r") as zipfp:
             for sep, fn in self.arcfiles.items():
-                with zipfp.open(fn, "rU") as fp:
+                with openU(zipfp, fn) as fp:
                     ziplines = fp.readlines()
                 for line, zipline in zip(self.line_gen, ziplines):
                     self.assertEqual(zipline, line + b'\n')
@@ -1682,7 +1697,7 @@
         # Read the ZIP archive
         with zipfile.ZipFile(f, "r") as zipfp:
             for sep, fn in self.arcfiles.items():
-                with zipfp.open(fn, "rU") as fp:
+                with openU(zipfp, fn) as fp:
                     for line, zipline in zip(self.line_gen, fp):
                         self.assertEqual(zipline, line + b'\n')