diff --git a/.ci/docker/manywheel/build_scripts/ssl-check.py b/.ci/docker/manywheel/build_scripts/ssl-check.py
index c4df0eacbb7f..0fd7eb363144 100644
--- a/.ci/docker/manywheel/build_scripts/ssl-check.py
+++ b/.ci/docker/manywheel/build_scripts/ssl-check.py
@@ -10,6 +10,11 @@ BAD_SSL = "https://self-signed.badssl.com"
 
 print("Testing SSL certificate checking for Python:", sys.version)
 
+if sys.version_info[:2] < (2, 7) or sys.version_info[:2] < (3, 4):
+    print("This version never checks SSL certs; skipping tests")
+    sys.exit(0)
+
+
 EXC = OSError
 
 print(f"Connecting to {GOOD_SSL} should work")
diff --git a/test/run_test.py b/test/run_test.py
index 4e246eda56e7..745e62331f30 100755
--- a/test/run_test.py
+++ b/test/run_test.py
@@ -951,7 +951,10 @@ def test_openreg(test_module, test_directory, options):
 
 
 def test_distributed(test_module, test_directory, options):
-    mpi_available = subprocess.call(["command", "-v", "mpiexec"]) == 0
+    # MPI tests are broken with Python-3.9
+    mpi_available = subprocess.call(
+        "command -v mpiexec", shell=True
+    ) == 0 and sys.version_info < (3, 9)
     if options.verbose and not mpi_available:
         print_to_stderr("MPI not available -- MPI backend tests will be skipped")