diff --git a/IPython/nbconvert/filters/tests/test_strings.py b/IPython/nbconvert/filters/tests/test_strings.py
index d4e0527..f93749c 100644
--- a/IPython/nbconvert/filters/tests/test_strings.py
+++ b/IPython/nbconvert/filters/tests/test_strings.py
@@ -88,12 +88,19 @@ class TestStrings(TestsBase):
             ('test="/files"', 'test="/files"'), 
             ('My files are in `files/`', 'My files are in `files/`'),
             ('<a href="files/test.html">files/test.html</a>', '<a href="test.html">files/test.html</a>'),
+            ('<a href="/files/test.html">files/test.html</a>', '<a href="test.html">files/test.html</a>'),
+            ("<a href='files/test.html'>files/test.html</a>", "<a href='test.html'>files/test.html</a>"),
+            ('<img src="files/url/location.gif">', '<img src="url/location.gif">'),
+            ('<img src="/files/url/location.gif">', '<img src="url/location.gif">'),
             ('hello![caption]', 'hello![caption]'),
             ('hello![caption](/url/location.gif)', 'hello![caption](/url/location.gif)'),
             ('hello![caption](url/location.gif)', 'hello![caption](url/location.gif)'),
             ('hello![caption](url/location.gif)', 'hello![caption](url/location.gif)'),
             ('hello![caption](files/url/location.gif)', 'hello![caption](url/location.gif)'),
-            ('hello![caption](/files/url/location.gif)', 'hello![caption](url/location.gif)'),]
+            ('hello![caption](/files/url/location.gif)', 'hello![caption](url/location.gif)'),
+            ('hello [text](/files/url/location.gif)', 'hello [text](url/location.gif)'),
+            ('hello [text space](files/url/location.gif)', 'hello [text space](url/location.gif)'),
+        ]
         for test in tests:
             self._try_files_prefix(test[0], test[1])