diff --git a/builtin/clone.c b/builtin/clone.c
index 0fc89ae2b9..0516181052 100644
--- a/builtin/clone.c
+++ b/builtin/clone.c
@@ -673,7 +673,7 @@ static void update_remote_refs(const struct ref *refs,
 			       const char *msg,
 			       struct transport *transport,
 			       int check_connectivity,
-			       int check_refs_only)
+			       int check_refs_are_promisor_objects_only)
 {
 	const struct ref *rm = mapped_refs;
 
@@ -682,7 +682,8 @@ static void update_remote_refs(const struct ref *refs,
 
 		opt.transport = transport;
 		opt.progress = transport->progress;
-		opt.check_refs_only = !!check_refs_only;
+		opt.check_refs_are_promisor_objects_only =
+			!!check_refs_are_promisor_objects_only;
 
 		if (check_connected(iterate_ref_map, &rm, &opt))
 			die(_("remote did not send all necessary objects"));
diff --git a/builtin/fetch.c b/builtin/fetch.c
index b4c6d921d0..6fb50320eb 100644
--- a/builtin/fetch.c
+++ b/builtin/fetch.c
@@ -906,8 +906,17 @@ static int store_updated_refs(const char *raw_url, const char *remote_name,
 		url = xstrdup("foreign");
 
 	if (!connectivity_checked) {
+		struct check_connected_options opt = CHECK_CONNECTED_INIT;
+
+		if (filter_options.choice)
+			/*
+			 * Since a filter is specified, objects indirectly
+			 * referenced by refs are allowed to be absent.
+			 */
+			opt.check_refs_are_promisor_objects_only = 1;
+
 		rm = ref_map;
-		if (check_connected(iterate_ref_map, &rm, NULL)) {
+		if (check_connected(iterate_ref_map, &rm, &opt)) {
 			rc = error(_("%s did not send all necessary objects\n"), url);
 			goto abort;
 		}
diff --git a/connected.c b/connected.c
index c337f5f7f4..7e9bd1bc62 100644
--- a/connected.c
+++ b/connected.c
@@ -52,19 +52,28 @@ int check_connected(oid_iterate_fn fn, void *cb_data,
 		strbuf_release(&idx_file);
 	}
 
-	if (opt->check_refs_only) {
+	if (opt->check_refs_are_promisor_objects_only) {
 		/*
 		 * For partial clones, we don't want to have to do a regular
 		 * connectivity check because we have to enumerate and exclude
 		 * all promisor objects (slow), and then the connectivity check
 		 * itself becomes a no-op because in a partial clone every
 		 * object is a promisor object. Instead, just make sure we
-		 * received the objects pointed to by each wanted ref.
+		 * received, in a promisor packfile, the objects pointed to by
+		 * each wanted ref.
 		 */
 		do {
-			if (!repo_has_object_file_with_flags(the_repository, &oid,
-							     OBJECT_INFO_SKIP_FETCH_OBJECT))
-				return 1;
+			struct packed_git *p;
+
+			for (p = get_all_packs(the_repository); p; p = p->next) {
+				if (!p->pack_promisor)
+					continue;
+				if (find_pack_entry_one(oid.hash, p))
+					goto promisor_pack_found;
+			}
+			return 1;
+promisor_pack_found:
+			;
 		} while (!fn(cb_data, &oid));
 		return 0;
 	}
diff --git a/connected.h b/connected.h
index ce2e7d8f2e..eba5c261ba 100644
--- a/connected.h
+++ b/connected.h
@@ -48,12 +48,13 @@ struct check_connected_options {
 	unsigned is_deepening_fetch : 1;
 
 	/*
-	 * If non-zero, only check the top-level objects referenced by the
-	 * wanted refs (passed in as cb_data). This is useful for partial
-	 * clones, where enumerating and excluding all promisor objects is very
-	 * slow and the commit-walk itself becomes a no-op.
+	 * If non-zero, only check that the top-level objects referenced by the
+	 * wanted refs (passed in as cb_data) are promisor objects. This is
+	 * useful for partial clones, where enumerating and excluding all
+	 * promisor objects is very slow and the commit-walk itself becomes a
+	 * no-op.
 	 */
-	unsigned check_refs_only : 1;
+	unsigned check_refs_are_promisor_objects_only : 1;
 };
 
 #define CHECK_CONNECTED_INIT { 0 }