diff --git a/test_zipp.py b/test_zipp.py
index 536f7d2..e35f06c 100644
--- a/test_zipp.py
+++ b/test_zipp.py
@@ -4,7 +4,6 @@
 
 import io
 import zipfile
-import posixpath
 import contextlib
 import tempfile
 import shutil
@@ -207,8 +206,8 @@ def test_mutability(self):
         for alpharep in self.zipfile_alpharep():
             root = zipp.Path(alpharep)
             a, b, g = root.iterdir()
-            alpharep.writestr('foo.txt', 'foo')
-            alpharep.writestr('bar/baz.txt', 'baz')
+            alpharep.writestr('foo.txt', b'foo')
+            alpharep.writestr('bar/baz.txt', b'baz')
             assert any(
                 child.name == 'foo.txt'
                 for child in root.iterdir())
diff --git a/zipp.py b/zipp.py
index 8c1b78d..2ede259 100644
--- a/zipp.py
+++ b/zipp.py
@@ -77,7 +77,7 @@ def _implied_dirs(names):
         return implied_dirs
 
     def namelist(self):
-        names = super().namelist()
+        names = super(CompleteDirs, self).namelist()
         return names + list(self._implied_dirs(names))
 
     def _name_set(self):
@@ -122,13 +122,13 @@ class FastLookup(CompleteDirs):
     def namelist(self):
         with suppress(AttributeError):
             return self.__names
-        self.__names = super().namelist()
+        self.__names = super(FastLookup, self).namelist()
         return self.__names
 
     def _name_set(self):
         with suppress(AttributeError):
             return self.__lookup
-        self.__lookup = super()._name_set()
+        self.__lookup = super(FastLookup, self)._name_set()
         return self.__lookup