diff --git a/.azure_pipeline.yml b/.azure_pipeline.yml
index ff01864b..5f1418a9 100644
--- a/.azure_pipeline.yml
+++ b/.azure_pipeline.yml
@@ -3,10 +3,10 @@ jobs:
   strategy:
     matrix:
 
-      # windows-py38:
-      #   imageName: "vs2017-win2016"
-      #   python.version: "3.8"
-      #   tox.env: py38
+      windows-py38:
+        imageName: "vs2017-win2016"
+        python.version: "3.8"
+        tox.env: py38
       windows-py35:
         imageName: "vs2017-win2016"
         python.version: "3.5"
@@ -16,10 +16,10 @@ jobs:
         python.version: "2.7"
         tox.env: py27
 
-      # macos-py38:
-      #   imageName: "macos-10.13"
-      #   python.version: "3.8"
-      #   tox.env: py38
+      macos-py38:
+        imageName: "macos-10.13"
+        python.version: "3.8"
+        tox.env: py38
       macos-py35:
         imageName: "macos-10.13"
         python.version: "3.5"
@@ -41,11 +41,11 @@ jobs:
         python.version: "3.8"
         tox.env: "py38"
         joblib.tests: "true"
-      # linux-py38-high-memory:
-      #   imageName: "ubuntu-16.04"
-      #   python.version: "3.8"
-      #   tox.env: py38
-      #   RUN_MEMORY: "true"
+      linux-py38-high-memory:
+        imageName: "ubuntu-16.04"
+        python.version: "3.8"
+        tox.env: py38
+        RUN_MEMORY: "true"
       linux-py37:
         imageName: "ubuntu-16.04"
         python.version: "3.7"
diff --git a/tests/_test_process_executor.py b/tests/_test_process_executor.py
index 16b1d5cc..55e1fe15 100644
--- a/tests/_test_process_executor.py
+++ b/tests/_test_process_executor.py
@@ -22,6 +22,7 @@
 import sys
 import time
 import shutil
+import platform
 import pytest
 import weakref
 import tempfile
@@ -535,9 +536,20 @@ def test_shutdown_race_issue12456(self):
         self.executor.map(str, [2] * (self.worker_count + 1))
         self.executor.shutdown()
 
+
+    @pytest.mark.skipif(
+            platform.python_implementation() != "CPython" or
+            (sys.version_info >= (3, 8, 0) and sys.version_info < (3, 8, 2)),
+            reason="Underlying bug fixed upstream starting Python 3.8.2")
     def test_no_stale_references(self):
         # Issue #16284: check that the executors don't unnecessarily hang onto
         # references.
+
+        # This test has to be skipped on early Python 3.8 versions because of a
+        # low-level reference cycle inside the pickle module for early versions
+        # of Python 3.8 preventing stale references from being collected. See
+        # cloudpipe/cloudpickle#327 as well as
+        # https://bugs.python.org/issue39492
         my_object = MyObject()
         collect = threading.Event()
         _ = weakref.ref(my_object, lambda obj: collect.set())  # noqa
@@ -793,11 +805,19 @@ def test_max_depth(self, kill_workers):
                                  ctx=self.context)
 
     @pytest.mark.high_memory
-    @pytest.mark.skipif(sys.version_info < (3, 4),
-                        reason="Limitation only present for python3")
-    def test_failure_on_large_data_send(self):
+    @pytest.mark.skipif(
+            sys.version_info[:2] < (3, 8),
+            reason="These Pythons cannot pickle objects of size > 2 ** 31GB")
+    def test_no_failure_on_large_data_send(self):
         data = b'\x00' * int(2.2e9)
+        self.executor.submit(id, data).result()
 
+    @pytest.mark.high_memory
+    @pytest.mark.skipif(
+            sys.version_info[:2] >= (3, 8),
+            reason="These Pythons can pickle objects of size > 2 ** 31GB")
+    def test_expected_failure_on_large_data_send(self):
+        data = b'\x00' * int(2.2e9)
         with pytest.raises(RuntimeError):
             self.executor.submit(id, data).result()