diff --git a/Lib/test/test_codecs.py b/Lib/test/test_codecs.py
index cf48637..9ae0ed0 100644
--- a/Lib/test/test_codecs.py
+++ b/Lib/test/test_codecs.py
@@ -642,6 +642,32 @@
 class UTF7Test(ReadTest):
     encoding = "utf-7"
 
+    def test_ascii(self):
+        # Set D (directly encoded characters)
+        set_d = ('ABCDEFGHIJKLMNOPQRSTUVWXYZ'
+                 'abcdefghijklmnopqrstuvwxyz'
+                 '0123456789'
+                 '\'(),-./:?')
+        self.assertEqual(set_d.encode(self.encoding), set_d)
+        self.assertEqual(set_d.decode(self.encoding), set_d)
+        # Set O (optional direct characters)
+        set_o = ' !"#$%&*;<=>@[]^_`{|}'
+        self.assertEqual(set_o.encode(self.encoding), set_o)
+        self.assertEqual(set_o.decode(self.encoding), set_o)
+        # +
+        self.assertEqual(u'a+b'.encode(self.encoding), 'a+-b')
+        self.assertEqual('a+-b'.decode(self.encoding), u'a+b')
+        # White spaces
+        ws = ' \t\n\r'
+        self.assertEqual(ws.encode(self.encoding), ws)
+        self.assertEqual(ws.decode(self.encoding), ws)
+        # Other ASCII characters
+        other_ascii = ''.join(sorted(set(chr(i) for i in range(0x80)) -
+                                     set(set_d + set_o + '+' + ws)))
+        self.assertEqual(other_ascii.encode(self.encoding),
+                         '+AAAAAQACAAMABAAFAAYABwAIAAsADAAOAA8AEAARABIAEwAU'
+                         'ABUAFgAXABgAGQAaABsAHAAdAB4AHwBcAH4Afw-')
+
     def test_partial(self):
         self.check_partial(
             u"a+-b",
@@ -656,7 +682,9 @@
 
     def test_errors(self):
         tests = [
+            ('\xffb', u'\ufffdb'),
             ('a\xffb', u'a\ufffdb'),
+            ('a\xff\xffb', u'a\ufffd\ufffdb'),
             ('a+IK', u'a\ufffd'),
             ('a+IK-b', u'a\ufffdb'),
             ('a+IK,b', u'a\ufffdb'),
@@ -672,6 +700,8 @@
             ('a+//,+IKw-b', u'a\ufffd\u20acb'),
             ('a+///,+IKw-b', u'a\uffff\ufffd\u20acb'),
             ('a+////,+IKw-b', u'a\uffff\ufffd\u20acb'),
+            ('a+IKw-b\xff', u'a\u20acb\ufffd'),
+            ('a+IKw\xffb', u'a\u20ac\ufffdb'),
         ]
         for raw, expected in tests:
             self.assertRaises(UnicodeDecodeError, codecs.utf_7_decode,
@@ -682,6 +712,35 @@
         self.assertEqual(u'\U000104A0'.encode(self.encoding), '+2AHcoA-')
         self.assertEqual(u'\ud801\udca0'.encode(self.encoding), '+2AHcoA-')
         self.assertEqual('+2AHcoA-'.decode(self.encoding), u'\U000104A0')
+        self.assertEqual('+2AHcoA'.decode(self.encoding), u'\U000104A0')
+        self.assertEqual(u'\u20ac\U000104A0'.encode(self.encoding), '+IKzYAdyg-')
+        self.assertEqual('+IKzYAdyg-'.decode(self.encoding), u'\u20ac\U000104A0')
+        self.assertEqual('+IKzYAdyg'.decode(self.encoding), u'\u20ac\U000104A0')
+        self.assertEqual(u'\u20ac\u20ac\U000104A0'.encode(self.encoding),
+                         '+IKwgrNgB3KA-')
+        self.assertEqual('+IKwgrNgB3KA-'.decode(self.encoding),
+                         u'\u20ac\u20ac\U000104A0')
+        self.assertEqual('+IKwgrNgB3KA'.decode(self.encoding),
+                         u'\u20ac\u20ac\U000104A0')
+
+    def test_lone_surrogates(self):
+        tests = [
+            ('a+2AE-b', u'a\ud801b'),
+            ('a+2AE\xffb', u'a\ufffdb'),
+            ('a+2AE', u'a\ufffd'),
+            ('a+2AEA-b', u'a\ufffdb'),
+            ('a+2AH-b', u'a\ufffdb'),
+            ('a+IKzYAQ-b', u'a\u20ac\ud801b'),
+            ('a+IKzYAQ\xffb', u'a\u20ac\ufffdb'),
+            ('a+IKzYAQA-b', u'a\u20ac\ufffdb'),
+            ('a+IKzYAd-b', u'a\u20ac\ufffdb'),
+            ('a+IKwgrNgB-b', u'a\u20ac\u20ac\ud801b'),
+            ('a+IKwgrNgB\xffb', u'a\u20ac\u20ac\ufffdb'),
+            ('a+IKwgrNgB', u'a\u20ac\u20ac\ufffd'),
+            ('a+IKwgrNgBA-b', u'a\u20ac\u20ac\ufffdb'),
+        ]
+        for raw, expected in tests:
+            self.assertEqual(raw.decode('utf-7', 'replace'), expected)
 
 class UTF16ExTest(unittest.TestCase):
 
diff --git a/Lib/test/test_unicode.py b/Lib/test/test_unicode.py
index 625d08c..be8f89b 100644
--- a/Lib/test/test_unicode.py
+++ b/Lib/test/test_unicode.py
@@ -1036,6 +1036,7 @@
         self.assertRaises(UnicodeError, unicode, 'Andr\202 x', 'ascii','strict')
         self.assertEqual(unicode('Andr\202 x','ascii','ignore'), u"Andr x")
         self.assertEqual(unicode('Andr\202 x','ascii','replace'), u'Andr\uFFFD x')
+        self.assertEqual(unicode('\202 x', 'ascii', 'replace'), u'\uFFFD x')
         self.assertEqual(u'abcde'.decode('ascii', 'ignore'),
                          u'abcde'.decode('ascii', errors='ignore'))
         self.assertEqual(u'abcde'.decode('ascii', 'replace'),
diff --git a/Misc/NEWS b/Misc/NEWS
index 7464870..0494fd1 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -10,6 +10,8 @@
 Core and Builtins
 -----------------
 
+- Issue #24848: Fixed a number of bugs in UTF-7 decoding of misformed data.
+
 - Issue #25003: os.urandom() doesn't use getentropy() on Solaris because
   getentropy() is blocking, whereas os.urandom() should not block. getentropy()
   is supported since Solaris 11.3.
diff --git a/Objects/unicodeobject.c b/Objects/unicodeobject.c
index 08723ac..6c46263 100644
--- a/Objects/unicodeobject.c
+++ b/Objects/unicodeobject.c
@@ -1716,29 +1716,29 @@
             }
             else { /* now leaving a base-64 section */
                 inShift = 0;
-                s++;
-                if (surrogate) {
-                    *p++ = surrogate;
-                    surrogate = 0;
-                }
                 if (base64bits > 0) { /* left-over bits */
                     if (base64bits >= 6) {
                         /* We've seen at least one base-64 character */
+                        s++;
                         errmsg = "partial character in shift sequence";
                         goto utf7Error;
                     }
                     else {
                         /* Some bits remain; they should be zero */
                         if (base64buffer != 0) {
+                            s++;
                             errmsg = "non-zero padding bits in shift sequence";
                             goto utf7Error;
                         }
                     }
                 }
-                if (ch != '-') {
+                if (surrogate && DECODE_DIRECT(ch))
+                    *p++ = surrogate;
+                surrogate = 0;
+                if (ch == '-') {
                     /* '-' is absorbed; other terminating
                        characters are preserved */
-                    *p++ = ch;
+                    s++;
                 }
             }
         }
@@ -1751,6 +1751,7 @@
             }
             else { /* begin base64-encoded section */
                 inShift = 1;
+                surrogate = 0;
                 shiftOutStart = p;
                 base64bits = 0;
                 base64buffer = 0;
@@ -1782,6 +1783,7 @@
 
     if (inShift && !consumed) { /* in shift sequence, no more to follow */
         /* if we're in an inconsistent state, that's an error */
+        inShift = 0;
         if (surrogate ||
                 (base64bits >= 6) ||
                 (base64bits > 0 && base64buffer != 0)) {