diff --git a/builtin/describe.c b/builtin/describe.c
index 7330a77b38ea7e..8ec3be87df0a2a 100644
--- a/builtin/describe.c
+++ b/builtin/describe.c
@@ -366,6 +366,12 @@ static void describe_commit(struct object_id *oid, struct strbuf *dst)
 		struct commit_name **slot;
 
 		seen_commits++;
+
+		if (match_cnt == max_candidates) {
+			gave_up_on = c;
+			break;
+		}
+
 		slot = commit_names_peek(&commit_names, c);
 		n = slot ? *slot : NULL;
 		if (n) {
@@ -381,10 +387,6 @@ static void describe_commit(struct object_id *oid, struct strbuf *dst)
 				if (n->prio == 2)
 					annotated_cnt++;
 			}
-			else {
-				gave_up_on = c;
-				break;
-			}
 		}
 		for (cur_match = 0; cur_match < match_cnt; cur_match++) {
 			struct possible_tag *t = &all_matches[cur_match];
@@ -470,9 +472,8 @@ static void describe_commit(struct object_id *oid, struct strbuf *dst)
 		fprintf(stderr, _("traversed %lu commits\n"), seen_commits);
 		if (gave_up_on) {
 			fprintf(stderr,
-				_("more than %i tags found; listed %i most recent\n"
-				"gave up search at %s\n"),
-				max_candidates, max_candidates,
+				_("found %i tags; gave up search at %s\n"),
+				max_candidates,
 				oid_to_hex(&gave_up_on->object.oid));
 		}
 	}
@@ -666,6 +667,8 @@ int cmd_describe(int argc,
 			     NULL);
 	if (!hashmap_get_size(&names) && !always)
 		die(_("No names found, cannot describe anything."));
+	if (hashmap_get_size(&names) < max_candidates)
+		max_candidates = hashmap_get_size(&names);
 
 	if (argc == 0) {
 		if (broken) {
diff --git a/t/perf/p6100-describe.sh b/t/perf/p6100-describe.sh
new file mode 100755
index 00000000000000..069f91ce493a70
--- /dev/null
+++ b/t/perf/p6100-describe.sh
@@ -0,0 +1,30 @@
+#!/bin/sh
+
+test_description='performance of git-describe'
+. ./perf-lib.sh
+
+test_perf_default_repo
+
+# clear out old tags and give us a known state
+test_expect_success 'set up tags' '
+	git for-each-ref --format="delete %(refname)" refs/tags >to-delete &&
+	git update-ref --stdin <to-delete &&
+	new=$(git rev-list -1000 HEAD | tail -n 1) &&
+	git tag -m new new $new &&
+	old=$(git rev-list       HEAD | tail -n 1) &&
+	git tag -m old old $old
+'
+
+test_perf 'describe HEAD' '
+	git describe HEAD
+'
+
+test_perf 'describe HEAD with one max candidate' '
+	git describe --candidates=1 HEAD
+'
+
+test_perf 'describe HEAD with one tag' '
+	git describe --match=new HEAD
+'
+
+test_done
diff --git a/t/t6120-describe.sh b/t/t6120-describe.sh
index 79e0f19deba0ef..5633b11d018b90 100755
--- a/t/t6120-describe.sh
+++ b/t/t6120-describe.sh
@@ -18,6 +18,7 @@ export GIT_TEST_DEFAULT_INITIAL_BRANCH_NAME
 
 check_describe () {
 	indir= &&
+	outcome=success &&
 	while test $# != 0
 	do
 		case "$1" in
@@ -25,6 +26,9 @@ check_describe () {
 			indir="$2"
 			shift
 			;;
+		--expect-failure)
+			outcome=failure
+			;;
 		*)
 			break
 			;;
@@ -35,7 +39,7 @@ check_describe () {
 	expect="$1"
 	shift
 	describe_opts="$@"
-	test_expect_success "describe $describe_opts" '
+	test_expect_${outcome} "describe $describe_opts" '
 		git ${indir:+ -C "$indir"} describe $describe_opts >raw &&
 		sed -e "s/-g[0-9a-f]*\$/-gHASH/" <raw >actual &&
 		echo "$expect" >expect &&
@@ -616,7 +620,7 @@ test_expect_success 'name-rev --annotate-stdin works with commitGraph' '
 
 #               B
 #               o
-#                \
+#  H             \
 #  o-----o---o----x
 #        A
 #
@@ -626,6 +630,7 @@ test_expect_success 'setup: describe commits with disjoint bases' '
 		cd disjoint1 &&
 
 		echo o >> file && git add file && git commit -m o &&
+		git tag H -a -m H &&
 		echo A >> file && git add file && git commit -m A &&
 		git tag A -a -m A &&
 		echo o >> file && git add file && git commit -m o &&
@@ -638,8 +643,9 @@ test_expect_success 'setup: describe commits with disjoint bases' '
 '
 
 check_describe -C disjoint1 "A-3-gHASH" HEAD
+check_describe -C disjoint1 --expect-failure "A-3-gHASH" --candidates=2 HEAD
 
-#           B
+#       H   B
 #   o---o---o------------.
 #                         \
 #                  o---o---x
@@ -657,6 +663,7 @@ test_expect_success 'setup: describe commits with disjoint bases 2' '
 		git checkout --orphan branch &&
 		echo o >> file2 && git add file2 && GIT_COMMITTER_DATE="2020-01-01 15:00" git commit -m o &&
 		echo o >> file2 && git add file2 && GIT_COMMITTER_DATE="2020-01-01 15:01" git commit -m o &&
+		git tag H -a -m H &&
 		echo B >> file2 && git add file2 && GIT_COMMITTER_DATE="2020-01-01 15:02" git commit -m B &&
 		git tag B -a -m B &&
 		git merge --no-ff --allow-unrelated-histories main -m x
@@ -664,6 +671,7 @@ test_expect_success 'setup: describe commits with disjoint bases 2' '
 '
 
 check_describe -C disjoint2 "B-3-gHASH" HEAD
+check_describe -C disjoint2 --expect-failure "B-3-gHASH" --candidates=2 HEAD
 
 test_expect_success 'setup misleading taggerdates' '
 	GIT_COMMITTER_DATE="2006-12-12 12:31" git tag -a -m "another tag" newer-tag-older-commit unique-file~1