diff --git a/tests/data/emitting-unacceptable-unicode-character-bug-py2.code b/tests/data/emitting-unacceptable-unicode-character-bug-ucs4-py2.code
similarity index 100%
rename from tests/data/emitting-unacceptable-unicode-character-bug-py2.code
rename to tests/data/emitting-unacceptable-unicode-character-bug-ucs4-py2.code
diff --git a/tests/data/emitting-unacceptable-unicode-character-bug-py2.data b/tests/data/emitting-unacceptable-unicode-character-bug-ucs4-py2.data
similarity index 100%
rename from tests/data/emitting-unacceptable-unicode-character-bug-py2.data
rename to tests/data/emitting-unacceptable-unicode-character-bug-ucs4-py2.data
diff --git a/tests/data/emitting-unacceptable-unicode-character-bug-py2.skip-ext b/tests/data/emitting-unacceptable-unicode-character-bug-ucs4-py2.skip-ext
similarity index 100%
rename from tests/data/emitting-unacceptable-unicode-character-bug-py2.skip-ext
rename to tests/data/emitting-unacceptable-unicode-character-bug-ucs4-py2.skip-ext
diff --git a/tests/data/emoticons.unicode b/tests/data/emoticons-ucs4-.unicode
similarity index 100%
rename from tests/data/emoticons.unicode
rename to tests/data/emoticons-ucs4-.unicode
diff --git a/tests/data/emoticons2.unicode b/tests/data/emoticons2-ucs4-.unicode
similarity index 100%
rename from tests/data/emoticons2.unicode
rename to tests/data/emoticons2-ucs4-.unicode
diff --git a/tests/lib/test_appliance.py b/tests/lib/test_appliance.py
index f69412c71..5ec457550 100644
--- a/tests/lib/test_appliance.py
+++ b/tests/lib/test_appliance.py
@@ -3,6 +3,8 @@
 
 DATA = 'tests/data'
 
+has_ucs4 = sys.maxunicode > 0xffff
+
 def find_test_functions(collections):
     if not isinstance(collections, list):
         collections = [collections]
@@ -25,6 +27,8 @@ def find_test_filenames(directory):
             base, ext = os.path.splitext(filename)
             if base.endswith('-py3'):
                 continue
+            if not has_ucs4 and base.find('-ucs4-') > -1:
+                continue
             filenames.setdefault(base, []).append(ext)
     filenames = filenames.items()
     filenames.sort()