diff --git a/Lib/test/test_import/__init__.py b/Lib/test/test_import/__init__.py
index 44e7da1033..85913cd7c5 100644
--- a/Lib/test/test_import/__init__.py
+++ b/Lib/test/test_import/__init__.py
@@ -457,6 +457,7 @@ def test_issue31492(self):
             with self.assertRaises(AttributeError):
                 os.does_not_exist
 
+    @unittest.skipIf(sys.platform == 'win32', 'TODO: RUSTPYTHON; Flaky')
     @threading_helper.requires_working_threading()
     def test_concurrency(self):
         # bpo 38091: this is a hack to slow down the code that calls
diff --git a/Lib/test/test_zipfile64.py b/Lib/test/test_zipfile64.py
index 0947013afb..2e1affe025 100644
--- a/Lib/test/test_zipfile64.py
+++ b/Lib/test/test_zipfile64.py
@@ -11,7 +11,7 @@
         'test requires loads of disk-space bytes and a long time to run'
     )
 
-import zipfile, os, unittest
+import zipfile, unittest
 import time
 import sys
 
@@ -32,10 +32,6 @@ def setUp(self):
         line_gen = ("Test of zipfile line %d." % i for i in range(1000000))
         self.data = '\n'.join(line_gen).encode('ascii')
 
-        # And write it to a file.
-        with open(TESTFN, "wb") as fp:
-            fp.write(self.data)
-
     def zipTest(self, f, compression):
         # Create the ZIP archive.
         with zipfile.ZipFile(f, "w", compression) as zipfp:
@@ -67,6 +63,9 @@ def zipTest(self, f, compression):
                     (num, filecount)), file=sys.__stdout__)
                     sys.__stdout__.flush()
 
+            # Check that testzip thinks the archive is valid
+            self.assertIsNone(zipfp.testzip())
+
     def testStored(self):
         # Try the temp file first.  If we do TESTFN2 first, then it hogs
         # gigabytes of disk space for the duration of the test.
@@ -85,9 +84,7 @@ def testDeflated(self):
         self.zipTest(TESTFN2, zipfile.ZIP_DEFLATED)
 
     def tearDown(self):
-        for fname in TESTFN, TESTFN2:
-            if os.path.exists(fname):
-                os.remove(fname)
+        os_helper.unlink(TESTFN2)
 
 
 class OtherTests(unittest.TestCase):