diff --git a/Lib/test/test_unicode.py b/Lib/test/test_unicode.py
--- a/Lib/test/test_unicode.py
+++ b/Lib/test/test_unicode.py
@@ -1091,10 +1091,18 @@ class UnicodeTest(string_tests.CommonTes
         for (x, y) in utfTests:
             self.assertEqual(x.encode('utf-7'), y)
 
-        # Unpaired surrogates not supported
-        self.assertRaises(UnicodeError, str, b'+3ADYAA-', 'utf-7')
+        # Unpaired surrogates are passed through
+        self.assertEqual('\uD801'.encode('utf-7'), b'+2AE-')
+        self.assertEqual('\uD801x'.encode('utf-7'), b'+2AE-x')
+        self.assertEqual('\uDC01'.encode('utf-7'), b'+3AE-')
+        self.assertEqual('\uDC01x'.encode('utf-7'), b'+3AE-x')
+        self.assertEqual(b'+2AE-'.decode('utf-7'), '\uD801')
+        self.assertEqual(b'+2AE-x'.decode('utf-7'), '\uD801x')
+        self.assertEqual(b'+3AE-'.decode('utf-7'), '\uDC01')
+        self.assertEqual(b'+3AE-x'.decode('utf-7'), '\uDC01x')
 
-        self.assertEqual(str(b'+3ADYAA-', 'utf-7', 'replace'), '\ufffd\ufffd')
+        self.assertEqual('\uD801\U000abcde'.encode('utf-7'), b'+2AHab9ze-')
+        self.assertEqual(b'+2AHab9ze-'.decode('utf-7'), '\uD801\U000abcde')
 
         # Issue #2242: crash on some Windows/MSVC versions
         self.assertEqual(b'+\xc1'.decode('utf-7'), '\xc1')
diff --git a/Objects/unicodeobject.c b/Objects/unicodeobject.c
--- a/Objects/unicodeobject.c
+++ b/Objects/unicodeobject.c
@@ -2284,19 +2284,15 @@ PyObject *PyUnicode_DecodeUTF7Stateful(c
                             surrogate = 0;
                         }
                         else {
+                            *p++ = surrogate;
+                            *p++ = outCh;
                             surrogate = 0;
-                            errmsg = "second surrogate missing";
-                            goto utf7Error;
                         }
                     }
                     else if (outCh >= 0xD800 && outCh <= 0xDBFF) {
                         /* first surrogate */
                         surrogate = outCh;
                     }
-                    else if (outCh >= 0xDC00 && outCh <= 0xDFFF) {
-                        errmsg = "unexpected second surrogate";
-                        goto utf7Error;
-                    }
                     else {
                         *p++ = outCh;
                     }
@@ -2306,8 +2302,8 @@ PyObject *PyUnicode_DecodeUTF7Stateful(c
                 inShift = 0;
                 s++;
                 if (surrogate) {
-                    errmsg = "second surrogate missing at end of shift sequence";
-                    goto utf7Error;
+                    *p++ = surrogate;
+                    surrogate = 0;
                 }
                 if (base64bits > 0) { /* left-over bits */
                     if (base64bits >= 6) {