diff --git a/builtin-fast-export.c b/builtin-fast-export.c
index 1ec459f05..f171ee4a2 100644
--- a/builtin-fast-export.c
+++ b/builtin-fast-export.c
@@ -362,7 +362,10 @@ static void get_tags_and_duplicates(struct object_array *pending,
 			break;
 		case OBJ_TAG:
 			tag = (struct tag *)e->item;
+
+			/* handle nested tags */
 			while (tag && tag->object.type == OBJ_TAG) {
+				parse_object(tag->object.sha1);
 				string_list_append(full_name, extra_refs)->util = tag;
 				tag = (struct tag *)tag->tagged;
 			}
@@ -375,7 +378,7 @@ static void get_tags_and_duplicates(struct object_array *pending,
 			case OBJ_BLOB:
 				handle_object(tag->object.sha1);
 				continue;
-			default:
+			default: /* OBJ_TAG (nested tags) is already handled */
 				warning("Tag points to object of unexpected type %s, skipping.",
 					typename(tag->object.type));
 				continue;
diff --git a/t/t9301-fast-export.sh b/t/t9301-fast-export.sh
index b1f75ceea..4a87f3625 100755
--- a/t/t9301-fast-export.sh
+++ b/t/t9301-fast-export.sh
@@ -271,7 +271,7 @@ test_expect_success 'set-up a few more tags for tag export tests' '
 # NEEDSWORK: not just check return status, but validate the output
 test_expect_success 'tree_tag'        'git fast-export tree_tag'
 test_expect_success 'tree_tag-obj'    'git fast-export tree_tag-obj'
-test_expect_failure 'tag-obj_tag'     'git fast-export tag-obj_tag'
-test_expect_failure 'tag-obj_tag-obj' 'git fast-export tag-obj_tag-obj'
+test_expect_success 'tag-obj_tag'     'git fast-export tag-obj_tag'
+test_expect_success 'tag-obj_tag-obj' 'git fast-export tag-obj_tag-obj'
 
 test_done