diff --git a/django/utils/html.py b/django/utils/html.py
index 13954ce195..0ee789ebb5 100644
--- a/django/utils/html.py
+++ b/django/utils/html.py
@@ -126,13 +126,13 @@ strip_tags = allow_lazy(strip_tags)
 def remove_tags(html, tags):
     """Returns the given HTML with given tags removed."""
     tags = [re.escape(tag) for tag in tags.split()]
-    tags_re = u'(%s)' % u'|'.join(tags)
-    starttag_re = re.compile(ur'<%s(/?>|(\s+[^>]*>))' % tags_re, re.U)
-    endtag_re = re.compile(u'</%s>' % tags_re)
-    html = starttag_re.sub(u'', html)
-    html = endtag_re.sub(u'', html)
+    tags_re = '(%s)' % '|'.join(tags)
+    starttag_re = re.compile(r'<%s(/?>|(\s+[^>]*>))' % tags_re, re.U)
+    endtag_re = re.compile('</%s>' % tags_re)
+    html = starttag_re.sub('', html)
+    html = endtag_re.sub('', html)
     return html
-remove_tags = allow_lazy(remove_tags, unicode)
+remove_tags = allow_lazy(remove_tags, six.text_type)
 
 def strip_spaces_between_tags(value):
     """Returns the given HTML with spaces between tags removed."""
diff --git a/django/utils/text.py b/django/utils/text.py
index cbafab0032..ca79a24f7c 100644
--- a/django/utils/text.py
+++ b/django/utils/text.py
@@ -391,7 +391,7 @@ def slugify(value):
     underscores) and converts spaces to hyphens. Also strips leading and
     trailing whitespace.
     """
-    value = unicodedata.normalize('NFKD', value).encode('ascii', 'ignore')
-    value = unicode(re.sub('[^\w\s-]', '', value).strip().lower())
+    value = unicodedata.normalize('NFKD', value).encode('ascii', 'ignore').decode('ascii')
+    value = re.sub('[^\w\s-]', '', value).strip().lower()
     return mark_safe(re.sub('[-\s]+', '-', value))
-slugify = allow_lazy(slugify, unicode)
+slugify = allow_lazy(slugify, six.text_type)
diff --git a/tests/regressiontests/utils/text.py b/tests/regressiontests/utils/text.py
index 9fa86d515c..ebf67952f9 100644
--- a/tests/regressiontests/utils/text.py
+++ b/tests/regressiontests/utils/text.py
@@ -116,8 +116,8 @@ class TestUtilsText(SimpleTestCase):
 
     def test_slugify(self):
         items = (
-            (u'Hello, World!', 'hello-world'),
-            (u'spam & eggs', 'spam-eggs'),
+            ('Hello, World!', 'hello-world'),
+            ('spam & eggs', 'spam-eggs'),
         )
         for value, output in items:
             self.assertEqual(text.slugify(value), output)