diff --git a/Lib/test/test_gzip.py b/Lib/test/test_gzip.py
index fa5de7c190e6a3..b347146ac9bec3 100644
--- a/Lib/test/test_gzip.py
+++ b/Lib/test/test_gzip.py
@@ -367,7 +367,7 @@ def test_metadata(self):
             self.assertEqual(cmByte, b'\x08') # deflate
 
             try:
-                expectedname = self.filename.encode('Latin-1') + b'\x00'
+                expectedname = os.path.basename(self.filename).encode('Latin-1') + b'\x00'
                 expectedflags = b'\x08' # only the FNAME flag is set
             except UnicodeEncodeError:
                 expectedname = b''
diff --git a/Lib/test/test_zlib.py b/Lib/test/test_zlib.py
index 4d97fe56f3a094..d7a071260dfccb 100644
--- a/Lib/test/test_zlib.py
+++ b/Lib/test/test_zlib.py
@@ -414,7 +414,7 @@ def test_decompimax(self, source=None, cx=256, dcx=64):
         dco = zlib.decompressobj()
         bufs = []
         cb = combuf
-        while cb:
+        while not dco.eof:
             #max_length = 1 + len(cb)//10
             chunk = dco.decompress(cb, dcx)
             self.assertFalse(len(chunk) > dcx,
@@ -439,7 +439,7 @@ def test_decompressmaxlen(self, flush=False):
         dco = zlib.decompressobj()
         bufs = []
         cb = combuf
-        while cb:
+        while not dco.eof:
             max_length = 1 + len(cb)//10
             chunk = dco.decompress(cb, max_length)
             self.assertFalse(len(chunk) > max_length,
@@ -449,7 +449,7 @@ def test_decompressmaxlen(self, flush=False):
         if flush:
             bufs.append(dco.flush())
         else:
-            while chunk:
+            while not dco.eof:
                 chunk = dco.decompress(b'', max_length)
                 self.assertFalse(len(chunk) > max_length,
                             'chunk too big (%d>%d)' % (len(chunk),max_length))