diff --git a/Lib/html/parser.py b/Lib/html/parser.py
index 5c4a7ef..a654780 100644
--- a/Lib/html/parser.py
+++ b/Lib/html/parser.py
@@ -23,6 +23,9 @@
 piclose = re.compile('>')
 commentclose = re.compile(r'--\s*>')
 tagfind = re.compile('[a-zA-Z][-.a-zA-Z0-9:_]*')
+# see http://www.w3.org/TR/html5/tokenization.html#tag-open-state
+# and http://www.w3.org/TR/html5/tokenization.html#tag-name-state
+tagfind_tolerant = re.compile('[a-zA-Z][^\t\n\r\f />\x00]*')
 # Note, the strict one of this pair isn't really strict, but we can't
 # make it correctly strict without breaking backward compatibility.
 attrfind = re.compile(
@@ -270,7 +273,7 @@
     # see http://www.w3.org/TR/html5/tokenization.html#bogus-comment-state
     def parse_bogus_comment(self, i, report=1):
         rawdata = self.rawdata
-        if rawdata[i:i+2] != '<!':
+        if rawdata[i:i+2] not in ('<!', '</'):
             self.error('unexpected call to parse_comment()')
         pos = rawdata.find('>', i+2)
         if pos == -1:
@@ -398,31 +401,40 @@
         match = endendtag.search(rawdata, i+1) # >
         if not match:
             return -1
-        j = match.end()
+        gtpos = match.end()
         match = endtagfind.match(rawdata, i) # </ + tag + >
         if not match:
             if self.cdata_elem is not None:
-                self.handle_data(rawdata[i:j])
-                return j
+                self.handle_data(rawdata[i:gtpos])
+                return gtpos
             if self.strict:
-                self.error("bad end tag: %r" % (rawdata[i:j],))
-            k = rawdata.find('<', i + 1, j)
-            if k > i:
-                j = k
-            if j <= i:
-                j = i + 1
-            self.handle_data(rawdata[i:j])
-            return j
+                self.error("bad end tag: %r" % (rawdata[i:gtpos],))
+            # find the name: w3.org/TR/html5/tokenization.html#tag-name-state
+            namematch = tagfind_tolerant.match(rawdata, i+2)
+            if not namematch:
+                # w3.org/TR/html5/tokenization.html#end-tag-open-state
+                if rawdata[i:i+3] == '</>':
+                    return i+3
+                else:
+                    return self.parse_bogus_comment(i)
+            tagname = namematch.group().lower()
+            # consume and ignore other stuff between the name and the >
+            # Note: this is not 100% correct, since we might have things like
+            # </tag attr=">">, but looking for > after tha name should cover
+            # most of the cases and is much simpler
+            gtpos = rawdata.find('>', namematch.end())
+            self.handle_endtag(tagname)
+            return gtpos+1
 
         elem = match.group(1).lower() # script or style
         if self.cdata_elem is not None:
             if elem != self.cdata_elem:
-                self.handle_data(rawdata[i:j])
-                return j
+                self.handle_data(rawdata[i:gtpos])
+                return gtpos
 
         self.handle_endtag(elem.lower())
         self.clear_cdata_mode()
-        return j
+        return gtpos
 
     # Overridable -- finish processing of start+end tag: <tag.../>
     def handle_startendtag(self, tag, attrs):
diff --git a/Lib/test/test_htmlparser.py b/Lib/test/test_htmlparser.py
index 7af9131..2e7277e 100644
--- a/Lib/test/test_htmlparser.py
+++ b/Lib/test/test_htmlparser.py
@@ -364,8 +364,9 @@
                             ('data', '<<bc'),
                             ('endtag', 'a'),
                             ('endtag', 'html'),
-                            ('data', '\n<img src="URL><//img></html'),
-                            ('endtag', 'html')])
+                            ('data', '\n<img src="URL>'),
+                            ('comment', '/img'),
+                            ('endtag', 'html<')])
 
     def test_with_unquoted_attributes(self):
         # see #12008
@@ -403,6 +404,44 @@
                             ('starttag', 'form',
                                 [('action', 'bogus|&#()value')])])
 
+    def test_invalid_end_tags(self):
+        # A collection of broken end tags. <br> is used as separator.
+        # see http://www.w3.org/TR/html5/tokenization.html#end-tag-open-state
+        # and #13993
+        html = ('<br></label</p><br></div end tmAd-leaderBoard><br></<h4><br>'
+                '</li class="unit"><br></li\r\n\t\t\t\t\t\t</ul><br></><br>')
+        expected = [('starttag', 'br', []),
+                    # < is part of the name, / is discarded, p is an attribute
+                    ('endtag', 'label<'),
+                    ('starttag', 'br', []),
+                    # text and attributes are discarded
+                    ('endtag', 'div'),
+                    ('starttag', 'br', []),
+                    # comment because the first char after </ is not a-zA-Z
+                    ('comment', '<h4'),
+                    ('starttag', 'br', []),
+                    # attributes are discarded
+                    ('endtag', 'li'),
+                    ('starttag', 'br', []),
+                    # everything till ul (included) is discarded
+                    ('endtag', 'li'),
+                    ('starttag', 'br', []),
+                    # </> is ignored
+                    ('starttag', 'br', [])]
+        self._run_check(html, expected)
+
+    def test_broken_invalid_end_tag(self):
+        # This is technically wrong (the "> shouldn't be included in the 'data')
+        # but is probably not worth fixing it (in addition to all the cases of
+        # the previous test, it would require a full attribute parsing).
+        # see #13993
+        html = '<b>This</b attr=">"> confuses the parser'
+        expected = [('starttag', 'b', []),
+                    ('data', 'This'),
+                    ('endtag', 'b'),
+                    ('data', '"> confuses the parser')]
+        self._run_check(html, expected)
+
     def test_correct_detection_of_start_tags(self):
         # see #13273
         html = ('<div style=""    ><b>The <a href="some_url">rain</a> '
diff --git a/Misc/NEWS b/Misc/NEWS
index 583673c..9294e70 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -113,6 +113,9 @@
 Library
 -------
 
+- Issue #13993: HTMLParser is now able to handle broken end tags when
+  strict=False.
+
 - Issue #9750: Fix sqlite3.Connection.iterdump on tables and fields
   with a name that is a keyword or contains quotes. Patch by Marko
   Kohtala.