diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 39cd114d3..e029104b3 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -20,8 +20,19 @@ jobs:
         os:
           - macos-latest
           - windows-latest
+          - ubuntu-latest
         python-version:
           - 2.7
+          - 3.6
+        exclude:
+          # Do not run coverage tests with Python 3.6 on Windows for
+          # now.  They will fail.  Dealing with them separately would
+          # be simpler.
+          #
+          # XXX: https://tahoe-lafs.org/trac/tahoe-lafs/ticket/3669
+          # should track the effort to add Windows to the test matrix.
+          - python-version: 3.6
+            os: windows-latest
 
     steps:
 
diff --git a/newsfragments/3616.minor b/newsfragments/3616.minor
new file mode 100644
index 000000000..e69de29bb