diff --git a/builtin/clone.c b/builtin/clone.c
index b93bcd460e1..143b4e0a3e7 100644
--- a/builtin/clone.c
+++ b/builtin/clone.c
@@ -657,7 +657,7 @@ static void write_followtags(const struct ref *refs, const char *msg)
 	}
 }
 
-static int iterate_ref_map(void *cb_data, struct object_id *oid)
+static const struct object_id *iterate_ref_map(void *cb_data)
 {
 	struct ref **rm = cb_data;
 	struct ref *ref = *rm;
@@ -668,13 +668,11 @@ static int iterate_ref_map(void *cb_data, struct object_id *oid)
 	 */
 	while (ref && !ref->peer_ref)
 		ref = ref->next;
-	/* Returning -1 notes "end of list" to the caller. */
 	if (!ref)
-		return -1;
+		return NULL;
 
-	oidcpy(oid, &ref->old_oid);
 	*rm = ref->next;
-	return 0;
+	return &ref->old_oid;
 }
 
 static void update_remote_refs(const struct ref *refs,
diff --git a/builtin/fetch.c b/builtin/fetch.c
index 38fab0369fa..75848d851db 100644
--- a/builtin/fetch.c
+++ b/builtin/fetch.c
@@ -854,13 +854,11 @@ static int update_local_ref(struct ref *ref,
 			    int summary_width)
 {
 	struct commit *current = NULL, *updated;
-	enum object_type type;
 	struct branch *current_branch = branch_get(NULL);
 	const char *pretty_ref = prettify_refname(ref->name);
 	int fast_forward = 0;
 
-	type = oid_object_info(the_repository, &ref->new_oid, NULL);
-	if (type < 0)
+	if (!repo_has_object_file(the_repository, &ref->new_oid))
 		die(_("object %s not found"), oid_to_hex(&ref->new_oid));
 
 	if (oideq(&ref->old_oid, &ref->new_oid)) {
@@ -972,7 +970,7 @@ static int update_local_ref(struct ref *ref,
 	}
 }
 
-static int iterate_ref_map(void *cb_data, struct object_id *oid)
+static const struct object_id *iterate_ref_map(void *cb_data)
 {
 	struct ref **rm = cb_data;
 	struct ref *ref = *rm;
@@ -980,10 +978,9 @@ static int iterate_ref_map(void *cb_data, struct object_id *oid)
 	while (ref && ref->status == REF_STATUS_REJECT_SHALLOW)
 		ref = ref->next;
 	if (!ref)
-		return -1; /* end of the list */
+		return NULL;
 	*rm = ref->next;
-	oidcpy(oid, &ref->old_oid);
-	return 0;
+	return &ref->old_oid;
 }
 
 struct fetch_head {
@@ -1082,7 +1079,6 @@ static int store_updated_refs(const char *raw_url, const char *remote_name,
 			      int connectivity_checked, struct ref *ref_map)
 {
 	struct fetch_head fetch_head;
-	struct commit *commit;
 	int url_len, i, rc = 0;
 	struct strbuf note = STRBUF_INIT, err = STRBUF_INIT;
 	struct ref_transaction *transaction = NULL;
@@ -1130,6 +1126,7 @@ static int store_updated_refs(const char *raw_url, const char *remote_name,
 	     want_status <= FETCH_HEAD_IGNORE;
 	     want_status++) {
 		for (rm = ref_map; rm; rm = rm->next) {
+			struct commit *commit = NULL;
 			struct ref *ref = NULL;
 
 			if (rm->status == REF_STATUS_REJECT_SHALLOW) {
@@ -1139,11 +1136,23 @@ static int store_updated_refs(const char *raw_url, const char *remote_name,
 				continue;
 			}
 
-			commit = lookup_commit_reference_gently(the_repository,
-								&rm->old_oid,
-								1);
-			if (!commit)
-				rm->fetch_head_status = FETCH_HEAD_NOT_FOR_MERGE;
+			/*
+			 * References in "refs/tags/" are often going to point
+			 * to annotated tags, which are not part of the
+			 * commit-graph. We thus only try to look up refs in
+			 * the graph which are not in that namespace to not
+			 * regress performance in repositories with many
+			 * annotated tags.
+			 */
+			if (!starts_with(rm->name, "refs/tags/"))
+				commit = lookup_commit_in_graph(the_repository, &rm->old_oid);
+			if (!commit) {
+				commit = lookup_commit_reference_gently(the_repository,
+									&rm->old_oid,
+									1);
+				if (!commit)
+					rm->fetch_head_status = FETCH_HEAD_NOT_FOR_MERGE;
+			}
 
 			if (rm->fetch_head_status != want_status)
 				continue;
@@ -1289,37 +1298,35 @@ static int check_exist_and_connected(struct ref *ref_map)
 	return check_connected(iterate_ref_map, &rm, &opt);
 }
 
-static int fetch_refs(struct transport *transport, struct ref *ref_map)
+static int fetch_and_consume_refs(struct transport *transport, struct ref *ref_map)
 {
-	int ret = check_exist_and_connected(ref_map);
+	int connectivity_checked = 1;
+	int ret;
+
+	/*
+	 * We don't need to perform a fetch in case we can already satisfy all
+	 * refs.
+	 */
+	ret = check_exist_and_connected(ref_map);
 	if (ret) {
 		trace2_region_enter("fetch", "fetch_refs", the_repository);
 		ret = transport_fetch_refs(transport, ref_map);
 		trace2_region_leave("fetch", "fetch_refs", the_repository);
+		if (ret)
+			goto out;
+		connectivity_checked = transport->smart_options ?
+			transport->smart_options->connectivity_checked : 0;
 	}
-	if (!ret)
-		/*
-		 * Keep the new pack's ".keep" file around to allow the caller
-		 * time to update refs to reference the new objects.
-		 */
-		return 0;
-	transport_unlock_pack(transport);
-	return ret;
-}
 
-/* Update local refs based on the ref values fetched from a remote */
-static int consume_refs(struct transport *transport, struct ref *ref_map)
-{
-	int connectivity_checked = transport->smart_options
-		? transport->smart_options->connectivity_checked : 0;
-	int ret;
 	trace2_region_enter("fetch", "consume_refs", the_repository);
 	ret = store_updated_refs(transport->url,
 				 transport->remote->name,
 				 connectivity_checked,
 				 ref_map);
-	transport_unlock_pack(transport);
 	trace2_region_leave("fetch", "consume_refs", the_repository);
+
+out:
+	transport_unlock_pack(transport);
 	return ret;
 }
 
@@ -1508,8 +1515,7 @@ static void backfill_tags(struct transport *transport, struct ref *ref_map)
 	transport_set_option(transport, TRANS_OPT_FOLLOWTAGS, NULL);
 	transport_set_option(transport, TRANS_OPT_DEPTH, "0");
 	transport_set_option(transport, TRANS_OPT_DEEPEN_RELATIVE, NULL);
-	if (!fetch_refs(transport, ref_map))
-		consume_refs(transport, ref_map);
+	fetch_and_consume_refs(transport, ref_map);
 
 	if (gsecondary) {
 		transport_disconnect(gsecondary);
@@ -1600,7 +1606,7 @@ static int do_fetch(struct transport *transport,
 				   transport->url);
 		}
 	}
-	if (fetch_refs(transport, ref_map) || consume_refs(transport, ref_map)) {
+	if (fetch_and_consume_refs(transport, ref_map)) {
 		free_refs(ref_map);
 		retcode = 1;
 		goto cleanup;
diff --git a/builtin/receive-pack.c b/builtin/receive-pack.c
index 2d1f97e1ca7..041e9154540 100644
--- a/builtin/receive-pack.c
+++ b/builtin/receive-pack.c
@@ -1306,7 +1306,7 @@ static void refuse_unconfigured_deny_delete_current(void)
 	rp_error("%s", _(refuse_unconfigured_deny_delete_current_msg));
 }
 
-static int command_singleton_iterator(void *cb_data, struct object_id *oid);
+static const struct object_id *command_singleton_iterator(void *cb_data);
 static int update_shallow_ref(struct command *cmd, struct shallow_info *si)
 {
 	struct shallow_lock shallow_lock = SHALLOW_LOCK_INIT;
@@ -1731,16 +1731,15 @@ static void check_aliased_updates(struct command *commands)
 	string_list_clear(&ref_list, 0);
 }
 
-static int command_singleton_iterator(void *cb_data, struct object_id *oid)
+static const struct object_id *command_singleton_iterator(void *cb_data)
 {
 	struct command **cmd_list = cb_data;
 	struct command *cmd = *cmd_list;
 
 	if (!cmd || is_null_oid(&cmd->new_oid))
-		return -1; /* end of list */
+		return NULL;
 	*cmd_list = NULL; /* this returns only one */
-	oidcpy(oid, &cmd->new_oid);
-	return 0;
+	return &cmd->new_oid;
 }
 
 static void set_connectivity_errors(struct command *commands,
@@ -1770,7 +1769,7 @@ struct iterate_data {
 	struct shallow_info *si;
 };
 
-static int iterate_receive_command_list(void *cb_data, struct object_id *oid)
+static const struct object_id *iterate_receive_command_list(void *cb_data)
 {
 	struct iterate_data *data = cb_data;
 	struct command **cmd_list = &data->cmds;
@@ -1781,13 +1780,11 @@ static int iterate_receive_command_list(void *cb_data, struct object_id *oid)
 			/* to be checked in update_shallow_ref() */
 			continue;
 		if (!is_null_oid(&cmd->new_oid) && !cmd->skip_update) {
-			oidcpy(oid, &cmd->new_oid);
 			*cmd_list = cmd->next;
-			return 0;
+			return &cmd->new_oid;
 		}
 	}
-	*cmd_list = NULL;
-	return -1; /* end of list */
+	return NULL;
 }
 
 static void reject_updates_to_hidden(struct command *commands)
diff --git a/connected.c b/connected.c
index b5f9523a5f8..cf68e37a97b 100644
--- a/connected.c
+++ b/connected.c
@@ -24,7 +24,7 @@ int check_connected(oid_iterate_fn fn, void *cb_data,
 	struct child_process rev_list = CHILD_PROCESS_INIT;
 	FILE *rev_list_in;
 	struct check_connected_options defaults = CHECK_CONNECTED_INIT;
-	struct object_id oid;
+	const struct object_id *oid;
 	int err = 0;
 	struct packed_git *new_pack = NULL;
 	struct transport *transport;
@@ -34,7 +34,8 @@ int check_connected(oid_iterate_fn fn, void *cb_data,
 		opt = &defaults;
 	transport = opt->transport;
 
-	if (fn(cb_data, &oid)) {
+	oid = fn(cb_data);
+	if (!oid) {
 		if (opt->err_fd)
 			close(opt->err_fd);
 		return err;
@@ -73,7 +74,7 @@ int check_connected(oid_iterate_fn fn, void *cb_data,
 			for (p = get_all_packs(the_repository); p; p = p->next) {
 				if (!p->pack_promisor)
 					continue;
-				if (find_pack_entry_one(oid.hash, p))
+				if (find_pack_entry_one(oid->hash, p))
 					goto promisor_pack_found;
 			}
 			/*
@@ -83,7 +84,7 @@ int check_connected(oid_iterate_fn fn, void *cb_data,
 			goto no_promisor_pack_found;
 promisor_pack_found:
 			;
-		} while (!fn(cb_data, &oid));
+		} while ((oid = fn(cb_data)) != NULL);
 		return 0;
 	}
 
@@ -133,12 +134,12 @@ int check_connected(oid_iterate_fn fn, void *cb_data,
 		 * are sure the ref is good and not sending it to
 		 * rev-list for verification.
 		 */
-		if (new_pack && find_pack_entry_one(oid.hash, new_pack))
+		if (new_pack && find_pack_entry_one(oid->hash, new_pack))
 			continue;
 
-		if (fprintf(rev_list_in, "%s\n", oid_to_hex(&oid)) < 0)
+		if (fprintf(rev_list_in, "%s\n", oid_to_hex(oid)) < 0)
 			break;
-	} while (!fn(cb_data, &oid));
+	} while ((oid = fn(cb_data)) != NULL);
 
 	if (ferror(rev_list_in) || fflush(rev_list_in)) {
 		if (errno != EPIPE && errno != EINVAL)
diff --git a/connected.h b/connected.h
index 8d5a6b3ad6f..6e59c92aa33 100644
--- a/connected.h
+++ b/connected.h
@@ -9,7 +9,7 @@ struct transport;
  * When called after returning the name for the last object, return -1
  * to signal EOF, otherwise return 0.
  */
-typedef int (*oid_iterate_fn)(void *, struct object_id *oid);
+typedef const struct object_id *(*oid_iterate_fn)(void *);
 
 /*
  * Named-arguments struct for check_connected. All arguments are
diff --git a/fetch-pack.c b/fetch-pack.c
index 0bf7ed7e477..a9604f35a3e 100644
--- a/fetch-pack.c
+++ b/fetch-pack.c
@@ -119,6 +119,11 @@ static struct commit *deref_without_lazy_fetch(const struct object_id *oid,
 {
 	enum object_type type;
 	struct object_info info = { .typep = &type };
+	struct commit *commit;
+
+	commit = lookup_commit_in_graph(the_repository, oid);
+	if (commit)
+		return commit;
 
 	while (1) {
 		if (oid_object_info_extended(the_repository, oid, &info,
@@ -1912,16 +1917,15 @@ static void update_shallow(struct fetch_pack_args *args,
 	oid_array_clear(&ref);
 }
 
-static int iterate_ref_map(void *cb_data, struct object_id *oid)
+static const struct object_id *iterate_ref_map(void *cb_data)
 {
 	struct ref **rm = cb_data;
 	struct ref *ref = *rm;
 
 	if (!ref)
-		return -1; /* end of the list */
+		return NULL;
 	*rm = ref->next;
-	oidcpy(oid, &ref->old_oid);
-	return 0;
+	return &ref->old_oid;
 }
 
 struct ref *fetch_pack(struct fetch_pack_args *args,