diff --git a/builtin/describe.c b/builtin/describe.c
index bffeed13a3..e93c3720ec 100644
--- a/builtin/describe.c
+++ b/builtin/describe.c
@@ -740,6 +740,9 @@ int cmd_describe(int argc,
 		return ret;
 	}
 
+	if (!all)
+		for_each_ref_opts.prefix = "refs/tags/";
+
 	hashmap_init(&names, commit_name_neq, NULL, 0);
 	refs_for_each_ref_ext(get_main_ref_store(the_repository),
 			      get_name, NULL, &for_each_ref_opts);
diff --git a/t/perf/p6100-describe.sh b/t/perf/p6100-describe.sh
index 069f91ce49..b1c61529bb 100755
--- a/t/perf/p6100-describe.sh
+++ b/t/perf/p6100-describe.sh
@@ -27,4 +27,16 @@ test_perf 'describe HEAD with one tag' '
 	git describe --match=new HEAD
 '
 
+test_expect_success 'set up many unrelated refs' '
+	ref_count=10000 &&
+	git tag -m tip tip HEAD &&
+	test_seq -f "create refs/heads/describe-perf/%05d HEAD" $ref_count |
+	git update-ref --stdin &&
+	git pack-refs --all
+'
+
+test_perf 'describe exact tag with many unrelated refs' '
+	git describe --exact-match HEAD
+'
+
 test_done