diff --git a/Lib/email/_header_value_parser.py b/Lib/email/_header_value_parser.py
index 9c55ef7fb45..51d355fbb0a 100644
--- a/Lib/email/_header_value_parser.py
+++ b/Lib/email/_header_value_parser.py
@@ -1218,12 +1218,21 @@ def get_bare_quoted_string(value):
         if value[0] in WSP:
             token, value = get_fws(value)
         elif value[:2] == '=?':
+            valid_ew = False
             try:
                 token, value = get_encoded_word(value)
                 bare_quoted_string.defects.append(errors.InvalidHeaderDefect(
                     "encoded word inside quoted string"))
+                valid_ew = True
             except errors.HeaderParseError:
                 token, value = get_qcontent(value)
+            # Collapse the whitespace between two encoded words that occur in a
+            # bare-quoted-string.
+            if valid_ew and len(bare_quoted_string) > 1:
+                if (bare_quoted_string[-1].token_type == 'fws' and
+                        bare_quoted_string[-2].token_type == 'encoded-word'):
+                    bare_quoted_string[-1] = EWWhiteSpaceTerminal(
+                        bare_quoted_string[-1], 'fws')
         else:
             token, value = get_qcontent(value)
         bare_quoted_string.append(token)
diff --git a/Lib/test/test_email/test_headerregistry.py b/Lib/test/test_email/test_headerregistry.py
index 82e121350ff..68bbc9561c4 100644
--- a/Lib/test/test_email/test_headerregistry.py
+++ b/Lib/test/test_email/test_headerregistry.py
@@ -873,6 +873,25 @@ class TestContentDisposition(TestHeaderBase):
             {'filename': 'foo'},
             [errors.InvalidHeaderDefect]),
 
+        'invalid_parameter_value_with_fws_between_ew': (
+            'attachment; filename="=?UTF-8?Q?Schulbesuchsbest=C3=A4ttigung=2E?='
+            '               =?UTF-8?Q?pdf?="',
+            'attachment',
+            {'filename': 'Schulbesuchsbestättigung.pdf'},
+            [errors.InvalidHeaderDefect]*3,
+            ('attachment; filename="Schulbesuchsbestättigung.pdf"'),
+            ('Content-Disposition: attachment;\n'
+             ' filename*=utf-8\'\'Schulbesuchsbest%C3%A4ttigung.pdf\n'),
+            ),
+
+        'parameter_value_with_fws_between_tokens': (
+            'attachment; filename="File =?utf-8?q?Name?= With Spaces.pdf"',
+            'attachment',
+            {'filename': 'File Name With Spaces.pdf'},
+            [errors.InvalidHeaderDefect],
+            'attachment; filename="File Name With Spaces.pdf"',
+            ('Content-Disposition: attachment; filename="File Name With Spaces.pdf"\n'),
+            )
     }
 
 
diff --git a/Misc/NEWS.d/next/Library/2019-12-15-18-47-20.bpo-39040.tKa0Qs.rst b/Misc/NEWS.d/next/Library/2019-12-15-18-47-20.bpo-39040.tKa0Qs.rst
new file mode 100644
index 00000000000..078bce22be3
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-12-15-18-47-20.bpo-39040.tKa0Qs.rst
@@ -0,0 +1,2 @@
+Fix parsing of invalid mime headers parameters by collapsing whitespace between
+encoded words in a bare-quote-string.