diff --git a/Lib/test/test_codeccallbacks.py b/Lib/test/test_codeccallbacks.py
index 56f3ac1..82782b5 100644
--- a/Lib/test/test_codeccallbacks.py
+++ b/Lib/test/test_codeccallbacks.py
@@ -153,28 +153,30 @@
             sout += bytes("\\U%08x" % sys.maxunicode, "ascii")
         self.assertEqual(sin.encode("iso-8859-15", "backslashreplace"), sout)
 
-    def test_decoderelaxedutf8(self):
-        # This is the test for a decoding callback handler,
-        # that relaxes the UTF-8 minimal encoding restriction.
-        # A null byte that is encoded as "\xc0\x80" will be
-        # decoded as a null byte. All other illegal sequences
-        # will be handled strictly.
+    def test_decoding_callbacks(self):
+        # This is a test for a decoding callback handler
+        # that allows the decoding of the invalid sequence
+        # "\xc0\x80" and returns "\x00" instead of raising an error.
+        # All other illegal sequences will be handled strictly.
         def relaxedutf8(exc):
             if not isinstance(exc, UnicodeDecodeError):
                 raise TypeError("don't know how to handle %r" % exc)
-            if exc.object[exc.start:exc.end].startswith(b"\xc0\x80"):
+            if exc.object[exc.start:exc.start+2] == b"\xc0\x80":
                 return ("\x00", exc.start+2) # retry after two bytes
             else:
                 raise exc
 
-        codecs.register_error(
-            "test.relaxedutf8", relaxedutf8)
+        codecs.register_error("test.relaxedutf8", relaxedutf8)
 
+        # all the "\xc0\x80" will be decoded to "\x00"
         sin = b"a\x00b\xc0\x80c\xc3\xbc\xc0\x80\xc0\x80"
         sout = "a\x00b\x00c\xfc\x00\x00"
         self.assertEqual(sin.decode("utf-8", "test.relaxedutf8"), sout)
+
+        # "\xc0\x81" is not valid and a UnicodeDecodeError will be raised
         sin = b"\xc0\x80\xc0\x81"
-        self.assertRaises(UnicodeError, sin.decode, "utf-8", "test.relaxedutf8")
+        self.assertRaises(UnicodeDecodeError, sin.decode,
+                          "utf-8", "test.relaxedutf8")
 
     def test_charmapencode(self):
         # For charmap encodings the replacement string will be
diff --git a/Lib/test/test_unicode.py b/Lib/test/test_unicode.py
index 788633f..ba66c81 100644
--- a/Lib/test/test_unicode.py
+++ b/Lib/test/test_unicode.py
@@ -942,6 +942,159 @@
         # * strict decoding testing for all of the
         #   UTF8_ERROR cases in PyUnicode_DecodeUTF8
 
+    def test_utf8_decode_valid_sequences(self):
+        sequences = [
+            # single byte
+            (b'\x00', '\x00'), (b'a', 'a'), (b'\x7f', '\x7f'),
+            # 2 bytes
+            (b'\xc2\x80', '\x80'), (b'\xdf\xbf', '\u07ff'),
+            # 3 bytes
+            (b'\xe0\xa0\x80', '\u0800'), (b'\xed\x9f\xbf', '\ud7ff'),
+            (b'\xee\x80\x80', '\uE000'), (b'\xef\xbf\xbf', '\uffff'),
+            # 4 bytes
+            (b'\xF0\x90\x80\x80', '\U00010000'),
+            (b'\xf4\x8f\xbf\xbf', '\U0010FFFF')
+        ]
+        for seq, res in sequences:
+            self.assertEqual(seq.decode('utf-8'), res)
+
+
+    def test_utf8_decode_invalid_sequences(self):
+        # continuation bytes in a sequence of 2, 3, or 4 bytes
+        continuation_bytes = [bytes([x]) for x in range(0x80, 0xC0)]
+        # start bytes of a 2-byte sequence equivalent to codepoints < 0x7F
+        invalid_2B_seq_start_bytes = [bytes([x]) for x in range(0xC0, 0xC2)]
+        # start bytes of a 4-byte sequence equivalent to codepoints > 0x10FFFF
+        invalid_4B_seq_start_bytes = [bytes([x]) for x in range(0xF5, 0xF8)]
+        invalid_start_bytes = (
+            continuation_bytes + invalid_2B_seq_start_bytes +
+            invalid_4B_seq_start_bytes + [bytes([x]) for x in range(0xF7, 0x100)]
+        )
+
+        for byte in invalid_start_bytes:
+            self.assertRaises(UnicodeDecodeError, byte.decode, 'utf-8')
+
+        for sb in invalid_2B_seq_start_bytes:
+            for cb in continuation_bytes:
+                self.assertRaises(UnicodeDecodeError, (sb+cb).decode, 'utf-8')
+
+        for sb in invalid_4B_seq_start_bytes:
+            for cb1 in continuation_bytes[:3]:
+                for cb3 in continuation_bytes[:3]:
+                    self.assertRaises(UnicodeDecodeError,
+                                      (sb+cb1+b'\x80'+cb3).decode, 'utf-8')
+
+        for cb in [bytes([x]) for x in range(0x80, 0xA0)]:
+            self.assertRaises(UnicodeDecodeError,
+                              (b'\xE0'+cb+b'\x80').decode, 'utf-8')
+            self.assertRaises(UnicodeDecodeError,
+                              (b'\xE0'+cb+b'\xBF').decode, 'utf-8')
+        # surrogates
+        for cb in [bytes([x]) for x in range(0xA0, 0xC0)]:
+            self.assertRaises(UnicodeDecodeError,
+                              (b'\xED'+cb+b'\x80').decode, 'utf-8')
+            self.assertRaises(UnicodeDecodeError,
+                              (b'\xED'+cb+b'\xBF').decode, 'utf-8')
+        for cb in [bytes([x]) for x in range(0x80, 0x90)]:
+            self.assertRaises(UnicodeDecodeError,
+                              (b'\xF0'+cb+b'\x80\x80').decode, 'utf-8')
+            self.assertRaises(UnicodeDecodeError,
+                              (b'\xF0'+cb+b'\xBF\xBF').decode, 'utf-8')
+        for cb in [bytes([x]) for x in range(0x90, 0xC0)]:
+            self.assertRaises(UnicodeDecodeError,
+                              (b'\xF4'+cb+b'\x80\x80').decode, 'utf-8')
+            self.assertRaises(UnicodeDecodeError,
+                              (b'\xF4'+cb+b'\xBF\xBF').decode, 'utf-8')
+
+    def test_issue8271(self):
+        # Issue #8271: during the decoding of an invalid UTF-8 byte sequence,
+        # only the start byte and the continuation byte(s) are now considered
+        # invalid, instead of the number of bytes specified by the start byte.
+        # See http://www.unicode.org/versions/Unicode5.2.0/ch03.pdf (page 95,
+        # table 3-8, Row 2) for more information about the algorithm used.
+        FFFD = '\ufffd'
+        sequences = [
+            # invalid start bytes
+            (b'\x80', FFFD), # continuation byte
+            (b'\x80\x80', FFFD*2), # 2 continuation bytes
+            (b'\xc0', FFFD),
+            (b'\xc0\xc0', FFFD*2),
+            (b'\xc1', FFFD),
+            (b'\xc1\xc0', FFFD*2),
+            (b'\xc0\xc1', FFFD*2),
+            # with start byte of a 2-byte sequence
+            (b'\xc2', FFFD), # only the start byte
+            (b'\xc2\xc2', FFFD*2), # 2 start bytes
+            (b'\xc2\xc2\xc2', FFFD*3), # 2 start bytes
+            (b'\xc2\x41', FFFD+'A'), # invalid continuation byte
+            # with start byte of a 3-byte sequence
+            (b'\xe1', FFFD), # only the start byte
+            (b'\xe1\xe1', FFFD*2), # 2 start bytes
+            (b'\xe1\xe1\xe1', FFFD*3), # 3 start bytes
+            (b'\xe1\xe1\xe1\xe1', FFFD*4), # 4 start bytes
+            (b'\xe1\x80', FFFD), # only 1 continuation byte
+            (b'\xe1\x41', FFFD+'A'), # invalid continuation byte
+            (b'\xe1\x41\x80', FFFD+'A'+FFFD), # invalid cb followed by valid cb
+            (b'\xe1\x41\x41', FFFD+'AA'), # 2 invalid continuation bytes
+            (b'\xe1\x80\x41', FFFD+'A'), # only 1 valid continuation byte
+            (b'\xe1\x80\xe1\x41', FFFD*2+'A'), # 1 valid and the other invalid
+            (b'\xe1\x41\xe1\x80', FFFD+'A'+FFFD), # 1 invalid and the other valid
+            # with start byte of a 4-byte sequence
+            (b'\xf1', FFFD), # only the start byte
+            (b'\xf1\xf1', FFFD*2), # 2 start bytes
+            (b'\xf1\xf1\xf1', FFFD*3), # 3 start bytes
+            (b'\xf1\xf1\xf1\xf1', FFFD*4), # 4 start bytes
+            (b'\xf1\xf1\xf1\xf1\xf1', FFFD*5), # 5 start bytes
+            (b'\xf1\x80', FFFD), # only 1 continuation bytes
+            (b'\xf1\x80\x80', FFFD), # only 2 continuation bytes
+            (b'\xf1\x80\x41', FFFD+'A'), # 1 valid cb and 1 invalid
+            (b'\xf1\x80\x41\x41', FFFD+'AA'), # 1 valid cb and 1 invalid
+            (b'\xf1\x80\x80\x41', FFFD+'A'), # 2 valid cb and 1 invalid
+            (b'\xf1\x41\x80', FFFD+'A'+FFFD), # 1 invalid cv and 1 valid
+            (b'\xf1\x41\x80\x80', FFFD+'A'+FFFD*2), # 1 invalid cb and 2 invalid
+            (b'\xf1\x41\x80\x41', FFFD+'A'+FFFD+'A'), # 2 invalid cb and 1 invalid
+            (b'\xf1\x41\x41\x80', FFFD+'AA'+FFFD), # 1 valid cb and 1 invalid
+            (b'\xf1\x41\xf1\x80', FFFD+'A'+FFFD),
+            (b'\xf1\x41\x80\xf1', FFFD+'A'+FFFD*2),
+            (b'\xf1\xf1\x80\x41', FFFD*2+'A'),
+            (b'\xf1\x41\xf1\xf1', FFFD+'A'+FFFD*2),
+            # with invalid start byte of a 4-byte sequence (rfc2279)
+            (b'\xf5', FFFD), # only the start byte
+            (b'\xf5\xf5', FFFD*2), # 2 start bytes
+            (b'\xf5\x80', FFFD*2), # only 1 continuation byte
+            (b'\xf5\x80\x80', FFFD*3), # only 2 continuation byte
+            (b'\xf5\x80\x80\x80', FFFD*4), # 3 continuation bytes
+            (b'\xf5\x80\x41', FFFD*2+'A'), #  1 valid cb and 1 invalid
+            (b'\xf5\x80\x41\xf5', FFFD*2+'A'+FFFD),
+            (b'\xf5\x41\x80\x80\x41', FFFD+'A'+FFFD*2+'A'),
+            # with invalid start byte of a 5-byte sequence (rfc2279)
+            (b'\xf8', FFFD), # only the start byte
+            (b'\xf8\xf8', FFFD*2), # 2 start bytes
+            (b'\xf8\x80', FFFD*2), # only one continuation byte
+            (b'\xf8\x80\x41', FFFD*2 + 'A'), # 1 valid cb and 1 invalid
+            (b'\xf8\x80\x80\x80\x80', FFFD*5), # invalid 5 bytes seq with 5 bytes
+            # with invalid start byte of a 6-byte sequence (rfc2279)
+            (b'\xfc', FFFD), # only the start byte
+            (b'\xfc\xfc', FFFD*2), # 2 start bytes
+            (b'\xfc\x80\x80', FFFD*3), # only 2 continuation bytes
+            (b'\xfc\x80\x80\x80\x80\x80', FFFD*6), # 6 continuation bytes
+            # invalid start byte
+            (b'\xfe', FFFD),
+            (b'\xfe\x80\x80', FFFD*3),
+            # other sequences
+            (b'\xf1\x80\x41\x42\x43', '\ufffd\x41\x42\x43'),
+            (b'\xf1\x80\xff\x42\x43', '\ufffd\ufffd\x42\x43'),
+            (b'\xf1\x80\xc2\x81\x43', '\ufffd\x81\x43'),
+            (b'\x61\xF1\x80\x80\xE1\x80\xC2\x62\x80\x63\x80\xBF\x64',
+             '\x61\uFFFD\uFFFD\uFFFD\x62\uFFFD\x63\uFFFD\uFFFD\x64'),
+        ]
+        for n, (seq, res) in enumerate(sequences):
+            self.assertRaises(UnicodeDecodeError, seq.decode, 'utf-8', 'strict')
+            self.assertEqual(seq.decode('utf-8', 'replace'), res)
+            self.assertEqual((seq+b'b').decode('utf-8', 'replace'), res+'b')
+            self.assertEqual(seq.decode('utf-8', 'ignore'),
+                             res.replace('\uFFFD', ''))
+
     def test_codecs_idna(self):
         # Test whether trailing dot is preserved
         self.assertEqual("www.python.org.".encode("idna"), b"www.python.org.")