diff --git a/Lib/_pyio.py b/Lib/_pyio.py
--- a/Lib/_pyio.py
+++ b/Lib/_pyio.py
@@ -181,8 +181,8 @@
     text = "t" in modes
     binary = "b" in modes
     if "U" in modes:
-        if creating or writing or appending:
-            raise ValueError("can't use U and writing mode at once")
+        if creating or writing or appending or updating:
+            raise ValueError("mode U cannot be combined with 'x', 'w', 'a', or '+'")
         import warnings
         warnings.warn("'U' mode is deprecated",
                       DeprecationWarning, 2)
diff --git a/Lib/test/test_file.py b/Lib/test/test_file.py
--- a/Lib/test/test_file.py
+++ b/Lib/test/test_file.py
@@ -139,7 +139,7 @@
 
     def testModeStrings(self):
         # check invalid mode strings
-        for mode in ("", "aU", "wU+"):
+        for mode in ("", "aU", "wU+", "U+", "+U", "rU+"):
             try:
                 f = self.open(TESTFN, mode)
             except ValueError:
diff --git a/Misc/NEWS b/Misc/NEWS
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -13,6 +13,9 @@
 Library
 -------
 
+- Issue #2091: open() accepted a 'U' mode string containing '+', but 'U' can
+  only be used with 'r'.
+
 - Issue #8585: improved tests for zipimporter2. Patch from Mark Lawrence.
 
 - Issue #18622: unittest.mock.mock_open().reset_mock would recurse infinitely.
diff --git a/Modules/_io/_iomodule.c b/Modules/_io/_iomodule.c
--- a/Modules/_io/_iomodule.c
+++ b/Modules/_io/_iomodule.c
@@ -307,9 +307,9 @@
 
     /* Parameters validation */
     if (universal) {
-        if (writing || appending) {
+        if (creating || writing || appending || updating) {
             PyErr_SetString(PyExc_ValueError,
-                            "can't use U and writing mode at once");
+                            "mode U cannot be combined with x', 'w', 'a', or '+'");
             return NULL;
         }
         if (PyErr_WarnEx(PyExc_DeprecationWarning,