diff --git a/builtin/pull.c b/builtin/pull.c
index efe4f4a81f..127798ba84 100644
--- a/builtin/pull.c
+++ b/builtin/pull.c
@@ -937,6 +937,33 @@ static int get_can_ff(struct object_id *orig_head,
 	return ret;
 }
 
+/*
+ * Is orig_head a descendant of _all_ merge_heads?
+ * Unfortunately is_descendant_of() cannot be used as it asks
+ * if orig_head is a descendant of at least one of them.
+ */
+static int already_up_to_date(struct object_id *orig_head,
+			      struct oid_array *merge_heads)
+{
+	int i;
+	struct commit *ours;
+
+	ours = lookup_commit_reference(the_repository, orig_head);
+	for (i = 0; i < merge_heads->nr; i++) {
+		struct commit_list *list = NULL;
+		struct commit *theirs;
+		int ok;
+
+		theirs = lookup_commit_reference(the_repository, &merge_heads->oid[i]);
+		commit_list_insert(theirs, &list);
+		ok = repo_is_descendant_of(the_repository, ours, list);
+		free_commit_list(list);
+		if (!ok)
+			return 0;
+	}
+	return 1;
+}
+
 static void show_advice_pull_non_ff(void)
 {
 	advise(_("You have divergent branches and need to specify how to reconcile them.\n"
@@ -1078,7 +1105,7 @@ int cmd_pull(int argc, const char **argv, const char *prefix)
 
 	/* ff-only takes precedence over rebase */
 	if (opt_ff && !strcmp(opt_ff, "--ff-only")) {
-		if (!can_ff)
+		if (!can_ff && !already_up_to_date(&orig_head, &merge_heads))
 			die_ff_impossible();
 		opt_rebase = REBASE_FALSE;
 	}
diff --git a/t/t7601-merge-pull-config.sh b/t/t7601-merge-pull-config.sh
index 1f652f433e..6275641b9c 100755
--- a/t/t7601-merge-pull-config.sh
+++ b/t/t7601-merge-pull-config.sh
@@ -2,7 +2,7 @@
 
 test_description='git merge
 
-Testing pull.* configuration parsing.'
+Testing pull.* configuration parsing and other things.'
 
 . ./test-lib.sh
 
@@ -387,6 +387,20 @@ test_expect_success 'pull prevents non-fast-forward with "only" in pull.ff' '
 	test_must_fail git pull . c3
 '
 
+test_expect_success 'already-up-to-date pull succeeds with "only" in pull.ff' '
+	git reset --hard c1 &&
+	test_config pull.ff only &&
+	git pull . c0 &&
+	test "$(git rev-parse HEAD)" = "$(git rev-parse c1)"
+'
+
+test_expect_success 'already-up-to-date pull/rebase succeeds with "only" in pull.ff' '
+	git reset --hard c1 &&
+	test_config pull.ff only &&
+	git -c pull.rebase=true pull . c0 &&
+	test "$(git rev-parse HEAD)" = "$(git rev-parse c1)"
+'
+
 test_expect_success 'merge c1 with c2 (ours in pull.twohead)' '
 	git reset --hard c1 &&
 	git config pull.twohead ours &&