diff --git a/loose.c b/loose.c
index bf01d3e42d..9dad75373b 100644
--- a/loose.c
+++ b/loose.c
@@ -61,9 +61,11 @@ static int insert_loose_map(struct odb_source_loose *loose,
 	return inserted;
 }
 
-static int load_one_loose_object_map(struct repository *repo, struct odb_source_loose *loose)
+static int load_one_loose_object_map(struct odb_source_loose *loose)
 {
-	struct strbuf buf = STRBUF_INIT, path = STRBUF_INIT;
+	struct repository *repo = loose->base.odb->repo;
+	struct strbuf buf = STRBUF_INIT;
+	char *path;
 	FILE *fp;
 	int ret = -1;
 
@@ -78,10 +80,10 @@ static int load_one_loose_object_map(struct repository *repo, struct odb_source_
 	insert_loose_map(loose, repo->hash_algo->empty_blob, repo->compat_hash_algo->empty_blob);
 	insert_loose_map(loose, repo->hash_algo->null_oid, repo->compat_hash_algo->null_oid);
 
-	repo_common_path_replace(repo, &path, "objects/loose-object-idx");
-	fp = fopen(path.buf, "rb");
+	path = xstrfmt("%s/loose-object-idx", loose->base.path);
+	fp = fopen(path, "rb");
 	if (!fp) {
-		strbuf_release(&path);
+		free(path);
 		return 0;
 	}
 
@@ -102,7 +104,7 @@ static int load_one_loose_object_map(struct repository *repo, struct odb_source_
 err:
 	fclose(fp);
 	strbuf_release(&buf);
-	strbuf_release(&path);
+	free(path);
 	return ret;
 }
 
@@ -117,10 +119,10 @@ int repo_read_loose_object_map(struct repository *repo)
 
 	for (source = repo->objects->sources; source; source = source->next) {
 		struct odb_source_files *files = odb_source_files_downcast(source);
-		if (load_one_loose_object_map(repo, files->loose) < 0) {
+		if (load_one_loose_object_map(files->loose) < 0)
 			return -1;
-		}
 	}
+
 	return 0;
 }
 
diff --git a/t/t1016-compatObjectFormat.sh b/t/t1016-compatObjectFormat.sh
index 92d48b96a1..9cafcee509 100755
--- a/t/t1016-compatObjectFormat.sh
+++ b/t/t1016-compatObjectFormat.sh
@@ -187,6 +187,24 @@ do
 		eval signedtag3_${hash}_oid=$(git hash-object -t tag -w ../${hash}_signedtag3) &&
 		eval signedtag4_${hash}_oid=$(git hash-object -t tag -w ../${hash}_signedtag4)
 	'
+
+	test_expect_success 'rev-parse maps oid of object borrowed from alternate' '
+		for repo in alt borrow
+		do
+			test_when_finished "rm -rf $repo" &&
+			git init --object-format=$hash $repo &&
+			git -C $repo config set core.repositoryformatversion 1 &&
+			git -C $repo config set extensions.compatObjectFormat $(compat_hash $hash) || exit 1
+		done &&
+
+		git -C alt commit --allow-empty --message A &&
+		echo "$(pwd)/alt/.git/objects" >borrow/.git/objects/info/alternates &&
+
+		oid=$(git -C alt rev-parse HEAD) &&
+		git -C alt    rev-parse --output-object-format=$(compat_hash $hash) "$oid" >expect &&
+		git -C borrow rev-parse --output-object-format=$(compat_hash $hash) "$oid" >actual &&
+		test_cmp expect actual
+	'
 done
 cd "$base"