diff --git a/markdownify/__init__.py b/markdownify/__init__.py
index 11c6270..6e842d8 100644
--- a/markdownify/__init__.py
+++ b/markdownify/__init__.py
@@ -5,6 +5,8 @@ import re
 convert_heading_re = re.compile(r'convert_h(\d+)')
 line_beginning_re = re.compile(r'^', re.MULTILINE)
 whitespace_re = re.compile(r'[\r\n\s\t ]+')
+FRAGMENT_ID = '__MARKDOWNIFY_WRAPPER__'
+wrapped = '<div id="%s">%%s</div>' % FRAGMENT_ID
 
 
 def escape(text):
@@ -22,10 +24,14 @@ class MarkdownConverter(object):
         self.tags_to_convert = tags_to_convert
 
     def convert(self, html):
+        # We want to take advantage of the html5 parsing, but we don't actually
+        # want a full document. Therefore, we'll mark our fragment with an id,
+        # create the document, and extract the element with the id.
+        html = wrapped % html
         soup = BeautifulSoup(html)
-        return self.process_tag(soup)
+        return self.process_tag(soup.find(id=FRAGMENT_ID), children_only=True)
 
-    def process_tag(self, node):
+    def process_tag(self, node, children_only=False):
         text = ''
 
         # Convert the children first
@@ -35,9 +41,10 @@ class MarkdownConverter(object):
             else:
                 text += self.process_tag(el)
 
-        convert_fn = getattr(self, 'convert_%s' % node.name, None)
-        if convert_fn and self.should_convert_tag(node.name):
-            text = convert_fn(node, text)
+        if not children_only:
+            convert_fn = getattr(self, 'convert_%s' % node.name, None)
+            if convert_fn and self.should_convert_tag(node.name):
+                text = convert_fn(node, text)
 
         return text