diff --git a/commit-reach.c b/commit-reach.c
index a34c5ba09e..399f2a8673 100644
--- a/commit-reach.c
+++ b/commit-reach.c
@@ -29,6 +29,10 @@ static int compare_commits_by_gen(const void *_a, const void *_b)
 		return -1;
 	if (generation_a > generation_b)
 		return 1;
+	if (a->date < b->date)
+		return -1;
+	if (a->date > b->date)
+		return 1;
 	return 0;
 }
 
@@ -228,11 +232,10 @@ static int remove_redundant_no_gen(struct repository *r,
 static int remove_redundant_with_gen(struct repository *r,
 				     struct commit **array, int cnt)
 {
-	int i, count_non_stale = 0;
+	int i, count_non_stale = 0, count_still_independent = cnt;
 	timestamp_t min_generation = GENERATION_NUMBER_INFINITY;
 	struct commit **walk_start;
 	size_t walk_start_nr = 0, walk_start_alloc = cnt;
-	struct prio_queue queue = { compare_commits_by_gen_then_commit_date };
 
 	ALLOC_ARRAY(walk_start, walk_start_alloc);
 
@@ -242,6 +245,7 @@ static int remove_redundant_with_gen(struct repository *r,
 		timestamp_t generation;
 
 		repo_parse_commit(r, array[i]);
+		array[i]->object.flags |= RESULT;
 		parents = array[i]->parents;
 
 		while (parents) {
@@ -250,7 +254,6 @@ static int remove_redundant_with_gen(struct repository *r,
 				parents->item->object.flags |= STALE;
 				ALLOC_GROW(walk_start, walk_start_nr + 1, walk_start_alloc);
 				walk_start[walk_start_nr++] = parents->item;
-				prio_queue_put(&queue, parents->item);
 			}
 			parents = parents->next;
 		}
@@ -261,26 +264,63 @@ static int remove_redundant_with_gen(struct repository *r,
 			min_generation = generation;
 	}
 
-	/* push the STALE bits up to min generation */
-	while (queue.nr) {
-		struct commit_list *parents;
-		struct commit *c = prio_queue_get(&queue);
+	QSORT(walk_start, walk_start_nr, compare_commits_by_gen);
 
-		repo_parse_commit(r, c);
+	/* remove STALE bit for now to allow walking through parents */
+	for (i = 0; i < walk_start_nr; i++)
+		walk_start[i]->object.flags &= ~STALE;
 
-		if (commit_graph_generation(c) < min_generation)
-			continue;
+	/*
+	 * Start walking from the highest generation. Hopefully, it will
+	 * find all other items during the first-parent walk, and we can
+	 * terminate early. Otherwise, we will do the same amount of work
+	 * as before.
+	 */
+	for (i = walk_start_nr - 1; i >= 0 && count_still_independent > 1; i--) {
+		/* push the STALE bits up to min generation */
+		struct commit_list *stack = NULL;
 
-		parents = c->parents;
-		while (parents) {
-			if (!(parents->item->object.flags & STALE)) {
-				parents->item->object.flags |= STALE;
-				prio_queue_put(&queue, parents->item);
+		commit_list_insert(walk_start[i], &stack);
+		walk_start[i]->object.flags |= STALE;
+
+		while (stack) {
+			struct commit_list *parents;
+			struct commit *c = stack->item;
+
+			repo_parse_commit(r, c);
+
+			if (c->object.flags & RESULT) {
+				c->object.flags &= ~RESULT;
+				if (--count_still_independent <= 1)
+					break;
 			}
-			parents = parents->next;
+
+			if (commit_graph_generation(c) < min_generation) {
+				pop_commit(&stack);
+				continue;
+			}
+
+			parents = c->parents;
+			while (parents) {
+				if (!(parents->item->object.flags & STALE)) {
+					parents->item->object.flags |= STALE;
+					commit_list_insert(parents->item, &stack);
+					break;
+				}
+				parents = parents->next;
+			}
+
+			/* pop if all parents have been visited already */
+			if (!parents)
+				pop_commit(&stack);
 		}
+		free_commit_list(stack);
 	}
 
+	/* clear result */
+	for (i = 0; i < cnt; i++)
+		array[i]->object.flags &= ~RESULT;
+
 	/* rearrange array */
 	for (i = count_non_stale = 0; i < cnt; i++) {
 		if (!(array[i]->object.flags & STALE))