diff --git a/Lib/email/_header_value_parser.py b/Lib/email/_header_value_parser.py
index 0392379..04ab84c 100644
--- a/Lib/email/_header_value_parser.py
+++ b/Lib/email/_header_value_parser.py
@@ -1556,6 +1556,13 @@
     while value and value[0] != '"':
         if value[0] in WSP:
             token, value = get_fws(value)
+        elif value[:2] == '=?':
+            try:
+                token, value = get_encoded_word(value)
+                bare_quoted_string.defects.append(errors.InvalidHeaderDefect(
+                    "encoded word inside quoted string"))
+            except errors.HeaderParseError:
+                token, value = get_qcontent(value)
         else:
             token, value = get_qcontent(value)
         bare_quoted_string.append(token)
diff --git a/Lib/test/test_email/test__header_value_parser.py b/Lib/test/test_email/test__header_value_parser.py
index 646082b..32996ca 100644
--- a/Lib/test/test_email/test__header_value_parser.py
+++ b/Lib/test/test_email/test__header_value_parser.py
@@ -540,6 +540,15 @@
         self._test_get_x(parser.get_bare_quoted_string,
             '""', '""', '', [], '')
 
+    # Issue 16983: apply postel's law to some bad encoding.
+    def test_encoded_word_inside_quotes(self):
+        self._test_get_x(parser.get_bare_quoted_string,
+            '"=?utf-8?Q?not_really_valid?="',
+            '"not really valid"',
+            'not really valid',
+            [errors.InvalidHeaderDefect],
+            '')
+
     # get_comment
 
     def test_get_comment_only(self):
diff --git a/Lib/test/test_email/test_headerregistry.py b/Lib/test/test_email/test_headerregistry.py
index f2df372..7d64a38 100644
--- a/Lib/test/test_email/test_headerregistry.py
+++ b/Lib/test/test_email/test_headerregistry.py
@@ -1155,6 +1155,16 @@
             'example.com',
             None),
 
+        'rfc2047_atom_in_quoted_string_is_decoded':
+            ('"=?utf-8?q?=C3=89ric?=" <foo@example.com>',
+            [errors.InvalidHeaderDefect],
+            'Éric <foo@example.com>',
+            'Éric',
+            'foo@example.com',
+            'foo',
+            'example.com',
+            None),
+
         }
 
         # XXX: Need many more examples, and in particular some with names in
diff --git a/Misc/NEWS b/Misc/NEWS
index 4df5a41..be6fee9 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -27,6 +27,9 @@
 Library
 -------
 
+- Issue #16983: the new email header parsing code will now decode encoded words
+  that are (incorrectly) surrounded by quotes, and register a defect.
+
 - Issue #19772: email.generator no longer mutates the message object when
   doing a down-transform from 8bit to 7bit CTEs.