diff --git a/builtin/prune.c b/builtin/prune.c
index 1ec9ddd751..04b6573945 100644
--- a/builtin/prune.c
+++ b/builtin/prune.c
@@ -31,16 +31,40 @@ static int prune_tmp_file(const char *fullpath)
 	return 0;
 }
 
-static int prune_object(const struct object_id *oid, const char *fullpath,
-			void *data)
+static void perform_reachability_traversal(struct rev_info *revs)
 {
-	struct stat st;
+	static int initialized;
+	struct progress *progress = NULL;
+
+	if (initialized)
+		return;
+
+	if (show_progress)
+		progress = start_delayed_progress(_("Checking connectivity"), 0);
+	mark_reachable_objects(revs, 1, expire, progress);
+	stop_progress(&progress);
+	initialized = 1;
+}
+
+static int is_object_reachable(const struct object_id *oid,
+			       struct rev_info *revs)
+{
+	perform_reachability_traversal(revs);
 
 	/*
 	 * Do we know about this object?
 	 * It must have been reachable
 	 */
-	if (lookup_object(the_repository, oid->hash))
+	return !!lookup_object(the_repository, oid->hash);
+}
+
+static int prune_object(const struct object_id *oid, const char *fullpath,
+			void *data)
+{
+	struct rev_info *revs = data;
+	struct stat st;
+
+	if (is_object_reachable(oid, revs))
 		return 0;
 
 	if (lstat(fullpath, &st)) {
@@ -102,7 +126,6 @@ static void remove_temporary_files(const char *path)
 int cmd_prune(int argc, const char **argv, const char *prefix)
 {
 	struct rev_info revs;
-	struct progress *progress = NULL;
 	int exclude_promisor_objects = 0;
 	const struct option options[] = {
 		OPT__DRY_RUN(&show_only, N_("do not remove, show only")),
@@ -142,17 +165,13 @@ int cmd_prune(int argc, const char **argv, const char *prefix)
 
 	if (show_progress == -1)
 		show_progress = isatty(2);
-	if (show_progress)
-		progress = start_delayed_progress(_("Checking connectivity"), 0);
 	if (exclude_promisor_objects) {
 		fetch_if_missing = 0;
 		revs.exclude_promisor_objects = 1;
 	}
 
-	mark_reachable_objects(&revs, 1, expire, progress);
-	stop_progress(&progress);
 	for_each_loose_file_in_objdir(get_object_directory(), prune_object,
-				      prune_cruft, prune_subdir, NULL);
+				      prune_cruft, prune_subdir, &revs);
 
 	prune_packed_objects(show_only ? PRUNE_PACKED_DRY_RUN : 0);
 	remove_temporary_files(get_object_directory());
@@ -160,8 +179,10 @@ int cmd_prune(int argc, const char **argv, const char *prefix)
 	remove_temporary_files(s);
 	free(s);
 
-	if (is_repository_shallow(the_repository))
+	if (is_repository_shallow(the_repository)) {
+		perform_reachability_traversal(&revs);
 		prune_shallow(show_only ? PRUNE_SHOW_ONLY : 0);
+	}
 
 	return 0;
 }
diff --git a/t/perf/p5304-prune.sh b/t/perf/p5304-prune.sh
new file mode 100755
index 0000000000..3c852084eb
--- /dev/null
+++ b/t/perf/p5304-prune.sh
@@ -0,0 +1,24 @@
+#!/bin/sh
+
+test_description='performance tests of prune'
+. ./perf-lib.sh
+
+test_perf_default_repo
+
+test_expect_success 'remove reachable loose objects' '
+	git repack -ad
+'
+
+test_expect_success 'remove unreachable loose objects' '
+	git prune
+'
+
+test_expect_success 'confirm there are no loose objects' '
+	git count-objects | grep ^0
+'
+
+test_perf 'prune with no objects' '
+	git prune
+'
+
+test_done
diff --git a/t/t5304-prune.sh b/t/t5304-prune.sh
index 270da21ac3..2c19a790c1 100755
--- a/t/t5304-prune.sh
+++ b/t/t5304-prune.sh
@@ -274,6 +274,18 @@ test_expect_success 'prune .git/shallow' '
 	test_path_is_missing .git/shallow
 '
 
+test_expect_success 'prune .git/shallow when there are no loose objects' '
+	SHA1=$(echo hi|git commit-tree HEAD^{tree}) &&
+	echo $SHA1 >.git/shallow &&
+	git update-ref refs/heads/shallow-tip $SHA1 &&
+	git repack -ad &&
+	# verify assumption that all loose objects are gone
+	git count-objects | grep ^0 &&
+	git prune &&
+	echo $SHA1 >expect &&
+	test_cmp expect .git/shallow
+'
+
 test_expect_success 'prune: handle alternate object database' '
 	test_create_repo A &&
 	git -C A commit --allow-empty -m "initial commit" &&