diff --git a/test/asynchronous/test_ssl.py b/test/asynchronous/test_ssl.py
index d920b77ac2..4d7566a61d 100644
--- a/test/asynchronous/test_ssl.py
+++ b/test/asynchronous/test_ssl.py
@@ -166,11 +166,14 @@ async def asyncTearDown(self):
 
     @async_client_context.require_tls
     async def test_simple_ssl(self):
+        if "PyPy" in sys.version:
+            self.skipTest("Test is flaky on PyPy")
         # Expects the server to be running with ssl and with
         # no --sslPEMKeyFile or with --sslWeakCertificateValidation
         await self.assertClientWorks(self.client)
 
     @async_client_context.require_tlsCertificateKeyFile
+    @async_client_context.require_no_api_version
     @ignore_deprecations
     async def test_tlsCertificateKeyFilePassword(self):
         # Expects the server to be running with server.pem and ca.pem
@@ -376,6 +379,7 @@ async def test_cert_ssl_validation_hostname_matching(self):
             )
 
     @async_client_context.require_tlsCertificateKeyFile
+    @async_client_context.require_no_api_version
     @ignore_deprecations
     async def test_tlsCRLFile_support(self):
         if not hasattr(ssl, "VERIFY_CRL_CHECK_LEAF") or _ssl.IS_PYOPENSSL:
@@ -531,6 +535,7 @@ def test_wincertstore(self):
 
     @async_client_context.require_auth
     @async_client_context.require_tlsCertificateKeyFile
+    @async_client_context.require_no_api_version
     @ignore_deprecations
     async def test_mongodb_x509_auth(self):
         host, port = await async_client_context.host, await async_client_context.port
@@ -640,6 +645,7 @@ async def test_mongodb_x509_auth(self):
             self.fail("Invalid certificate accepted.")
 
     @async_client_context.require_tlsCertificateKeyFile
+    @async_client_context.require_no_api_version
     @ignore_deprecations
     async def test_connect_with_ca_bundle(self):
         def remove(path):
diff --git a/test/test_ssl.py b/test/test_ssl.py
index a66fe21be5..7decc8203d 100644
--- a/test/test_ssl.py
+++ b/test/test_ssl.py
@@ -166,11 +166,14 @@ def tearDown(self):
 
     @client_context.require_tls
     def test_simple_ssl(self):
+        if "PyPy" in sys.version:
+            self.skipTest("Test is flaky on PyPy")
         # Expects the server to be running with ssl and with
         # no --sslPEMKeyFile or with --sslWeakCertificateValidation
         self.assertClientWorks(self.client)
 
     @client_context.require_tlsCertificateKeyFile
+    @client_context.require_no_api_version
     @ignore_deprecations
     def test_tlsCertificateKeyFilePassword(self):
         # Expects the server to be running with server.pem and ca.pem
@@ -376,6 +379,7 @@ def test_cert_ssl_validation_hostname_matching(self):
             )
 
     @client_context.require_tlsCertificateKeyFile
+    @client_context.require_no_api_version
     @ignore_deprecations
     def test_tlsCRLFile_support(self):
         if not hasattr(ssl, "VERIFY_CRL_CHECK_LEAF") or _ssl.IS_PYOPENSSL:
@@ -531,6 +535,7 @@ def test_wincertstore(self):
 
     @client_context.require_auth
     @client_context.require_tlsCertificateKeyFile
+    @client_context.require_no_api_version
     @ignore_deprecations
     def test_mongodb_x509_auth(self):
         host, port = client_context.host, client_context.port
@@ -640,6 +645,7 @@ def test_mongodb_x509_auth(self):
             self.fail("Invalid certificate accepted.")
 
     @client_context.require_tlsCertificateKeyFile
+    @client_context.require_no_api_version
     @ignore_deprecations
     def test_connect_with_ca_bundle(self):
         def remove(path):