diff --git a/t/README b/t/README
index 44c02d8129..8dcb778e26 100644
--- a/t/README
+++ b/t/README
@@ -386,6 +386,9 @@ GIT_TEST_PASSING_SANITIZE_LEAK=check when combined with "--immediate"
 will run to completion faster, and result in the same failing
 tests.
 
+GIT_TEST_PASSING_SANITIZE_LEAK=check-failing behaves the same as "check",
+but skips all tests which are already marked as leak-free.
+
 GIT_TEST_PROTOCOL_VERSION=<n>, when set, makes 'protocol.version'
 default to n.
 
diff --git a/t/test-lib.sh b/t/test-lib.sh
index 54247604cb..64bd36531c 100644
--- a/t/test-lib.sh
+++ b/t/test-lib.sh
@@ -1558,8 +1558,16 @@ then
 		passes_sanitize_leak=t
 	fi
 
-	if test "$GIT_TEST_PASSING_SANITIZE_LEAK" = "check"
+	if test "$GIT_TEST_PASSING_SANITIZE_LEAK" = "check" ||
+	   test "$GIT_TEST_PASSING_SANITIZE_LEAK" = "check-failing"
 	then
+		if test "$GIT_TEST_PASSING_SANITIZE_LEAK" = "check-failing" &&
+		   test -n "$passes_sanitize_leak"
+		then
+			skip_all="skipping leak-free $this_test under GIT_TEST_PASSING_SANITIZE_LEAK=check-failing"
+			test_done
+		fi
+
 		sanitize_leak_check=t
 		if test -n "$invert_exit_code"
 		then
@@ -1597,6 +1605,7 @@ then
 	export LSAN_OPTIONS
 
 elif test "$GIT_TEST_PASSING_SANITIZE_LEAK" = "check" ||
+     test "$GIT_TEST_PASSING_SANITIZE_LEAK" = "check-failing" ||
      test_bool_env GIT_TEST_PASSING_SANITIZE_LEAK false
 then
 	BAIL_OUT_ENV_NEEDS_SANITIZE_LEAK "GIT_TEST_PASSING_SANITIZE_LEAK=true"