diff --git a/dodgy/checks.py b/dodgy/checks.py
index 93474e9..918590c 100644
--- a/dodgy/checks.py
+++ b/dodgy/checks.py
@@ -67,8 +67,11 @@ def check_line(line, check_list):
 
 
 def check_file(filepath):
-    with open(filepath) as to_check:
-        return check_file_contents(to_check.read())
+    try:
+        with open(filepath) as to_check:
+            return check_file_contents(to_check.read())
+    except UnicodeDecodeError as e:
+        return [(0, 'unicode_decode_error', str(e))]
 
 
 def check_file_contents(file_contents):
diff --git a/dodgy/run.py b/dodgy/run.py
index 55fb332..f284600 100644
--- a/dodgy/run.py
+++ b/dodgy/run.py
@@ -40,6 +40,9 @@ def run_checks(directory, ignore_paths=None):
         mimetype = mimetypes.guess_type(filepath)
         if mimetype[0] is None or not mimetype[0].startswith('text/'):
             continue
+        # Also skip anything with an encoding (e.g., a gzipped CSS).
+        if mimetype[1]:
+            continue
 
         for msg_parts in check_file(filepath):
             warnings.append({
diff --git a/tests/test_checks.py b/tests/test_checks.py
index 79b3be8..dc800d8 100644
--- a/tests/test_checks.py
+++ b/tests/test_checks.py
@@ -1,4 +1,5 @@
 import os
+import sys
 from unittest import TestCase
 from dodgy.checks import check_file
 
@@ -48,3 +49,10 @@ def test_ssh_privatekey(self):
 
     def test_ssh_publickey(self):
         self._do_test('ssh_public_key.pub', 'ssh_rsa_public_key')
+
+    def test_bad_unicode(self):
+        """Test that we handle errors during Python 3's required Unicode
+        decoding."""
+        if sys.version_info > (3, 0):
+            self._do_test('bad_utf8.txt', 'unicode_decode_error')
+
diff --git a/tests/testdata/bad_utf8.txt b/tests/testdata/bad_utf8.txt
new file mode 100644
index 0000000..06c0962
--- /dev/null
+++ b/tests/testdata/bad_utf8.txt
@@ -0,0 +1 @@
+Ã(
\ No newline at end of file
diff --git a/tox.ini b/tox.ini
index 7c78e47..f6c7f3d 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = py26,py27,py33
+envlist = py26,py27,py33,py34
 
 [testenv]
 deps=nose