diff --git a/Lib/sgmllib.py b/Lib/sgmllib.py
index 3ab57c2..3020d11 100644
--- a/Lib/sgmllib.py
+++ b/Lib/sgmllib.py
@@ -29,7 +29,12 @@
 shorttagopen = re.compile('<[a-zA-Z][-.a-zA-Z0-9]*/')
 shorttag = re.compile('<([a-zA-Z][-.a-zA-Z0-9]*)/([^/]*)/')
 piclose = re.compile('>')
-endbracket = re.compile('[<>]')
+starttag = re.compile(r'<[a-zA-Z][-_.:a-zA-Z0-9]*\s*('
+        r'\s*([a-zA-Z_][-:.a-zA-Z_0-9]*)(\s*=\s*'
+        r'(\'[^\']*\'|"[^"]*"|[-a-zA-Z0-9./,:;+*%?!&$\(\)_#=~@]'
+        r'[][\-a-zA-Z0-9./,:;+*%?!&$\(\)_#=~\'"@]*(?=[\s>/<])))?'
+    r')*\s*/?\s*(?=[<>])')
+endtag = re.compile(r'</?[a-zA-Z][-_.:a-zA-Z0-9]*\s*/?\s*(?=[<>])')
 tagfind = re.compile('[a-zA-Z][-_.a-zA-Z0-9]*')
 attrfind = re.compile(
     r'\s*([a-zA-Z_][-:.a-zA-Z_0-9]*)(\s*=\s*'
@@ -249,14 +254,10 @@
             self.finish_shorttag(tag, data)
             self.__starttag_text = rawdata[start_pos:match.end(1) + 1]
             return k
-        # XXX The following should skip matching quotes (' or ")
-        # As a shortcut way to exit, this isn't so bad, but shouldn't
-        # be used to locate the actual end of the start tag since the
-        # < or > characters may be embedded in an attribute value.
-        match = endbracket.search(rawdata, i+1)
+        match = starttag.match(rawdata, i)
         if not match:
             return -1
-        j = match.start(0)
+        j = match.end(0)
         # Now parse the data between i+1 and j into a tag and attrs
         attrs = []
         if rawdata[i:i+2] == '<>':
@@ -305,10 +306,10 @@
     # Internal -- parse endtag
     def parse_endtag(self, i):
         rawdata = self.rawdata
-        match = endbracket.search(rawdata, i+1)
+        match = endtag.match(rawdata, i)
         if not match:
             return -1
-        j = match.start(0)
+        j = match.end(0)
         tag = rawdata[i+2:j].strip().lower()
         if rawdata[j] == '>':
             j = j+1
diff --git a/Lib/test/test_sgmllib.py b/Lib/test/test_sgmllib.py
index 076df37..28a21a4 100644
--- a/Lib/test/test_sgmllib.py
+++ b/Lib/test/test_sgmllib.py
@@ -286,6 +286,21 @@
             ('codepoint', 'convert', 42),
             ])
 
+    def test_attr_values_quoted_markup(self):
+        """Multi-line and markup in attribute values"""
+        self.check_events("""<a title='foo\n<br>bar'>text</a>""",
+            [("starttag", "a", [("title", "foo\n<br>bar")]),
+             ("data", "text"),
+             ("endtag", "a")])
+        self.check_events("""<a title='less < than'>text</a>""",
+            [("starttag", "a", [("title", "less < than")]),
+             ("data", "text"),
+             ("endtag", "a")])
+        self.check_events("""<a title='greater > than'>text</a>""",
+            [("starttag", "a", [("title", "greater > than")]),
+             ("data", "text"),
+             ("endtag", "a")])
+
     def test_attr_funky_names(self):
         self.check_events("""<a a.b='v' c:d=v e-f=v>""", [
             ("starttag", "a", [("a.b", "v"), ("c:d", "v"), ("e-f", "v")]),