diff --git a/test/runtimes/proctor/lib/python.go b/test/runtimes/proctor/lib/python.go
index 0684331c9..668996e57 100644
--- a/test/runtimes/proctor/lib/python.go
+++ b/test/runtimes/proctor/lib/python.go
@@ -58,9 +58,10 @@ var exclude = map[string][]string{
 	"test_fcntl": []string{"TestFcntl.test_fcntl_64_bit"},
 	// TODO(b/76174079): Un-exclude once this bug is fixed.
 	"test_posix": []string{
-		"PosixTester.test_fs_holes",
+		"PosixTester.test_fs_holes", // Fails only with --overlay=none.
 		"PosixTester.test_sched_priority",
 		"PosixTester.test_sched_rr_get_interval",
+		"PosixTester.test_get_and_set_scheduler_and_param", // sched_setparam(2) is not supported.
 		"TestPosixSpawn.test_setscheduler_only_param",
 		"TestPosixSpawnP.test_setscheduler_only_param",
 	},
diff --git a/test/runtimes/runner/lib/lib.go b/test/runtimes/runner/lib/lib.go
index ab71f162b..2ca8f84fc 100644
--- a/test/runtimes/runner/lib/lib.go
+++ b/test/runtimes/runner/lib/lib.go
@@ -116,7 +116,7 @@ func getTests(ctx context.Context, d *dockerutil.Container, lang, image string,
 		panic("TIMEOUT: Unable to get a list of tests")
 	}()
 	// Get a list of all tests in the image.
-	list, err := d.Exec(ctx, dockerutil.ExecOpts{}, "/proctor/proctor", "--runtime", lang, "--list")
+	list, err := d.Exec(ctx, dockerutil.ExecOpts{Privileged: true, User: "0"}, "/proctor/proctor", "--runtime", lang, "--list")
 	if err != nil {
 		return nil, fmt.Errorf("docker exec failed: %v", err)
 	}
@@ -188,7 +188,7 @@ func getTests(ctx context.Context, d *dockerutil.Container, lang, image string,
 						fmt.Sprintf("--timeout=%s", timeout-time.Since(startTime)),
 					}
 					argv = append(argv, proctorSettings.ToArgs()...)
-					output, err = d.Exec(ctx, dockerutil.ExecOpts{}, argv...)
+					output, err = d.Exec(ctx, dockerutil.ExecOpts{Privileged: true, User: "0"}, argv...)
 					close(done)
 				}()