diff --git a/t/t0061-run-command.sh b/t/t0061-run-command.sh
index 17e969df60..9acf628726 100755
--- a/t/t0061-run-command.sh
+++ b/t/t0061-run-command.sh
@@ -34,7 +34,7 @@ test_expect_success POSIXPERM 'run_command reports EACCES' '
 	grep "fatal: cannot exec.*hello.sh" err
 '
 
-test_expect_success POSIXPERM 'unreadable directory in PATH' '
+test_expect_success POSIXPERM,SANITY 'unreadable directory in PATH' '
 	mkdir local-command &&
 	test_when_finished "chmod u+rwx local-command && rm -fr local-command" &&
 	git config alias.nitfol "!echo frotz" &&
diff --git a/t/t1509-root-worktree.sh b/t/t1509-root-worktree.sh
index 335420fd87..b6977d4b39 100755
--- a/t/t1509-root-worktree.sh
+++ b/t/t1509-root-worktree.sh
@@ -98,8 +98,16 @@ test_foobar_foobar() {
 	'
 }
 
-if ! test_have_prereq POSIXPERM || ! [ -w / ]; then
-	skip_all="Dangerous test skipped. Read this test if you want to execute it"
+if ! test -w /
+then
+	skip_all="Test requiring writable / skipped. Read this test if you want to run it"
+	test_done
+fi
+
+if  test -e /refs || test -e /objects || test -e /info || test -e /hooks ||
+    test -e /.git || test -e /foo || test -e /me
+then
+	skip_all="Skip test that clobbers existing files in /"
 	test_done
 fi
 
@@ -108,8 +116,9 @@ if [ "$IKNOWWHATIAMDOING" != "YES" ]; then
 	test_done
 fi
 
-if [ "$UID" = 0 ]; then
-	skip_all="No you can't run this with root"
+if ! test_have_prereq NOT_ROOT
+then
+	skip_all="No you can't run this as root"
 	test_done
 fi