diff --git a/.ci/azure-pipelines.yml b/.ci/azure-pipelines.yml
index 397c52f3..5f687be4 100644
--- a/.ci/azure-pipelines.yml
+++ b/.ci/azure-pipelines.yml
@@ -66,6 +66,12 @@ jobs:
         DISTRO: debian
         VER: 2.10.0
 
+      Mito39Debian_27:
+        python.version: '3.9'
+        MODE: mitogen
+        DISTRO: debian
+        VER: 2.10.0
+
       #Py26CentOS7:
         #python.version: '2.7'
         #MODE: mitogen
@@ -117,3 +123,8 @@ jobs:
         python.version: '3.5'
         MODE: ansible
         VER: 2.10.0
+
+      Ansible_210_39:
+        python.version: '3.9'
+        MODE: ansible
+        VER: 2.10.0
diff --git a/.travis.yml b/.travis.yml
index aafb4413..7ee98677 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,5 +1,5 @@
 sudo: required
-dist: trusty
+dist: xenial  # Ubuntu 16.04 LTS
 
 notifications:
   email: false
@@ -17,7 +17,6 @@ cache:
   - /home/travis/virtualenv
 
 install:
-- grep -Erl git-lfs\|couchdb /etc/apt | sudo xargs rm -v
 - pip install -U pip==20.2.1
 - .ci/${MODE}_install.py
 
@@ -53,6 +52,9 @@ matrix:
     - python: "3.6"
       env: MODE=ansible VER=2.10.0
     # 2.10 -> {debian, centos6, centos7}
+    - python: "3.9"
+      env: MODE=ansible VER=2.10.0
+    # 2.10 -> {debian, centos6, centos7}
     - python: "2.7"
       env: MODE=ansible VER=2.10.0
     # 2.10 -> {debian, centos6, centos7}
@@ -73,6 +75,8 @@ matrix:
       #env: MODE=mitogen DISTRO=centos6
     - python: "3.6"
       env: MODE=mitogen DISTROS=centos7 VER=2.10.0
+    - python: "3.9"
+      env: MODE=mitogen DISTROS=centos7 VER=2.10.0
     # 2.6 -> 2.7
     # - python: "2.6"
     #   env: MODE=mitogen DISTROS=centos7 VER=2.10.0
diff --git a/docs/changelog.rst b/docs/changelog.rst
index 4cb8d6fe..99c30798 100644
--- a/docs/changelog.rst
+++ b/docs/changelog.rst
@@ -40,6 +40,8 @@ v0.2.10 (unreleased)
   timeout, when using recent OpenSSH client versions.
 * :gh:issue:`758` fix initilialisation of callback plugins in test suite, to address a `KeyError` in
   :method:`ansible.plugins.callback.CallbackBase.v2_runner_on_start`
+* :gh:issue:`775` Test with Python 3.9
+* :gh:issue:`775` Add msvcrt to the default module deny list
 
 
 v0.2.9 (2019-11-02)
diff --git a/mitogen/core.py b/mitogen/core.py
index 4dd44925..9a00ce65 100644
--- a/mitogen/core.py
+++ b/mitogen/core.py
@@ -1269,6 +1269,13 @@ class Importer(object):
         # a negative round-trip.
         'builtins',
         '__builtin__',
+
+        # On some Python releases (e.g. 3.8, 3.9) the subprocess module tries
+        # to import of this Windows-only builtin module.
+        'msvcrt',
+
+        # Python 2.x module that was renamed to _thread in 3.x.
+        # This entry avoids a roundtrip on 2.x -> 3.x.
         'thread',
 
         # org.python.core imported by copy, pickle, xml.sax; breaks Jython, but
diff --git a/tests/ansible/requirements.txt b/tests/ansible/requirements.txt
index c0386cd8..2c3c87c8 100644
--- a/tests/ansible/requirements.txt
+++ b/tests/ansible/requirements.txt
@@ -1,4 +1,4 @@
 paramiko==2.3.2  # Last 2.6-compat version.
 hdrhistogram==0.6.1
 PyYAML==3.11; python_version < '2.7'
-PyYAML==3.13; python_version >= '2.7'
+PyYAML==5.3.1; python_version >= '2.7'  # Latest release (Jan 2021)
diff --git a/tests/testlib.py b/tests/testlib.py
index ace8f0a2..ee76a26d 100644
--- a/tests/testlib.py
+++ b/tests/testlib.py
@@ -103,6 +103,18 @@ if hasattr(subprocess.Popen, 'terminate'):
     Popen__terminate = subprocess.Popen.terminate
 
 
+def threading__thread_is_alive(thread):
+    """Return whether the thread is alive (Python version compatibility shim).
+
+    On Python >= 3.8 thread.isAlive() is deprecated (removed in Python 3.9).
+    On Python <= 2.5 thread.is_alive() isn't present (added in Python 2.6).
+    """
+    try:
+        return thread.is_alive()
+    except AttributeError:
+        return thread.isAlive()
+
+
 def wait_for_port(
         host,
         port,
@@ -334,7 +346,9 @@ class TestCase(unittest2.TestCase):
         for thread in threading.enumerate():
             name = thread.getName()
             # Python 2.4: enumerate() may return stopped threads.
-            assert (not thread.isAlive()) or name in self.ALLOWED_THREADS, \
+            assert \
+                not threading__thread_is_alive(thread) \
+                or name in self.ALLOWED_THREADS, \
                 'Found thread %r still running after tests.' % (name,)
             counts[name] = counts.get(name, 0) + 1
 
diff --git a/tests/utils_test.py b/tests/utils_test.py
index a70b23dc..b5204a3c 100644
--- a/tests/utils_test.py
+++ b/tests/utils_test.py
@@ -31,14 +31,14 @@ class RunWithRouterTest(testlib.TestCase):
     def test_run_with_broker(self):
         router = mitogen.utils.run_with_router(func0)
         self.assertIsInstance(router, mitogen.master.Router)
-        self.assertFalse(router.broker._thread.isAlive())
+        self.assertFalse(testlib.threading__thread_is_alive(router.broker._thread))
 
 
 class WithRouterTest(testlib.TestCase):
     def test_with_broker(self):
         router = func()
         self.assertIsInstance(router, mitogen.master.Router)
-        self.assertFalse(router.broker._thread.isAlive())
+        self.assertFalse(testlib.threading__thread_is_alive(router.broker._thread))
 
 
 class Dict(dict): pass