diff --git a/.github/workflows/python-ci.yml b/.github/workflows/python-ci.yml
index 37d9c09..e6a0e32 100644
--- a/.github/workflows/python-ci.yml
+++ b/.github/workflows/python-ci.yml
@@ -39,13 +39,6 @@ jobs:
             os: macos-latest
           - python-version: "3.7"
             os: macos-latest
-        include: # So run those legacy versions on Intel CPUs.
-          - python-version: "3.5"
-            os: macos-13
-          - python-version: "3.6"
-            os: macos-13
-          - python-version: "3.7"
-            os: macos-13
 
     steps:
       - uses: actions/checkout@v5
diff --git a/configcatclienttests/test_autopollingcachepolicy.py b/configcatclienttests/test_autopollingcachepolicy.py
index b6e0553..d8f921a 100644
--- a/configcatclienttests/test_autopollingcachepolicy.py
+++ b/configcatclienttests/test_autopollingcachepolicy.py
@@ -59,7 +59,8 @@ def test_init_wait_time_timeout(self):
         end_time = time.time()
         elapsed_time = end_time - start_time
         self.assertEqual(config, None)
-        self.assertGreaterEqual(elapsed_time, 1)
+        wait_tolerance = 0.1
+        self.assertGreaterEqual(elapsed_time, 1 - wait_tolerance)
         self.assertLess(elapsed_time, 2)
         cache_policy.close()
 
@@ -69,7 +70,7 @@ def test_fetch_call_count(self):
         cache_policy = ConfigService('', PollingMode.auto_poll(poll_interval_seconds=2,
                                                                max_init_wait_time_seconds=1),
                                      Hooks(), config_fetcher, log, config_cache, False)
-        wait_tolerance = 0.1
+        wait_tolerance = 0.3
         time.sleep(3 + wait_tolerance)
         self.assertEqual(config_fetcher.get_call_count, 2)
         config, _ = cache_policy.get_config()
@@ -126,7 +127,8 @@ def test_rerun(self):
         cache_policy = ConfigService('', PollingMode.auto_poll(poll_interval_seconds=2,
                                                                max_init_wait_time_seconds=5),
                                      Hooks(), config_fetcher, log, config_cache, False)
-        time.sleep(2.200)
+        wait_tolerance = 0.4
+        time.sleep(2 + wait_tolerance)
         self.assertEqual(config_fetcher.get_call_count, 2)
         cache_policy.close()
 
@@ -141,13 +143,14 @@ def test_callback(self):
                                                                max_init_wait_time_seconds=5),
                                      hooks, config_fetcher, log, config_cache, False)
         time.sleep(1)
+        wait_tolerance = 0.3
         self.assertEqual(config_fetcher.get_call_count, 1)
         self.assertEqual(hook_callbacks.changed_config_call_count, 1)
-        time.sleep(1.2)
+        time.sleep(1 + wait_tolerance)
         self.assertEqual(config_fetcher.get_call_count, 2)
         self.assertEqual(hook_callbacks.changed_config_call_count, 1)
         config_fetcher.set_configuration_json(TEST_JSON2)
-        time.sleep(2.2)
+        time.sleep(2 + wait_tolerance)
         self.assertEqual(config_fetcher.get_call_count, 3)
         self.assertEqual(hook_callbacks.changed_config_call_count, 2)
         cache_policy.close()
@@ -162,14 +165,15 @@ def test_callback_exception(self):
         cache_policy = ConfigService('', PollingMode.auto_poll(poll_interval_seconds=2,
                                                                max_init_wait_time_seconds=5),
                                      hooks, config_fetcher, log, config_cache, False)
+        wait_tolerance = 0.4
         time.sleep(1)
         self.assertEqual(config_fetcher.get_call_count, 1)
         self.assertEqual(hook_callbacks.callback_exception_call_count, 1)
-        time.sleep(1.2)
+        time.sleep(1 + wait_tolerance)
         self.assertEqual(config_fetcher.get_call_count, 2)
         self.assertEqual(hook_callbacks.callback_exception_call_count, 1)
         config_fetcher.set_configuration_json(TEST_JSON2)
-        time.sleep(2.2)
+        time.sleep(2 + wait_tolerance)
         self.assertEqual(config_fetcher.get_call_count, 3)
         self.assertEqual(hook_callbacks.callback_exception_call_count, 2)
         cache_policy.close()
@@ -232,7 +236,8 @@ def test_return_cached_config_when_cache_is_not_expired(self):
         self.assertEqual(config_fetcher.get_call_count, 0)
         self.assertEqual(config_fetcher.get_fetch_count, 0)
 
-        time.sleep(3)
+        wait_tolerance = 0.1
+        time.sleep(3 + wait_tolerance)
 
         config, _ = cache_policy.get_config()
         settings = config.get(FEATURE_FLAGS)