diff --git a/Documentation/rev-list-options.adoc b/Documentation/rev-list-options.adoc
index eaee6ee8399c57..6df0e536ad7ce6 100644
--- a/Documentation/rev-list-options.adoc
+++ b/Documentation/rev-list-options.adoc
@@ -223,9 +223,10 @@ explicitly.
 	Pretend as if all objects mentioned as ref tips of alternate
 	repositories were listed on the command line. An alternate
 	repository is any repository whose object directory is specified
-	in `objects/info/alternates`.  The set of included objects may
-	be modified by `core.alternateRefsCommand`, etc. See
-	linkgit:git-config[1].
+	in `objects/info/alternates`.  The refs of shallow and grafted
+	alternate repositories are ignored, as the history behind them
+	may be missing.  The set of included objects may be modified by
+	`core.alternateRefsCommand`, etc. See linkgit:git-config[1].
 
 `--single-worktree`::
 	By default, all working trees will be examined by the
diff --git a/connected.c b/connected.c
index 7e269768327238..cf2647c94244b6 100644
--- a/connected.c
+++ b/connected.c
@@ -91,15 +91,17 @@ int check_connected(oid_iterate_fn fn, void *cb_data,
 	strvec_push(&rev_list.args, "--stdin");
 	if (repo_has_promisor_remote(the_repository))
 		strvec_push(&rev_list.args, "--exclude-promisor-objects");
+
+	/* define where the traversal should stop */
+	strvec_push(&rev_list.args, "--not");
 	if (!opt->is_deepening_fetch) {
-		strvec_push(&rev_list.args, "--not");
 		if (opt->exclude_hidden_refs_section)
 			strvec_pushf(&rev_list.args, "--exclude-hidden=%s",
 				     opt->exclude_hidden_refs_section);
 		strvec_push(&rev_list.args, "--all");
 	}
-	strvec_push(&rev_list.args, "--quiet");
 	strvec_push(&rev_list.args, "--alternate-refs");
+	strvec_push(&rev_list.args, "--quiet");
 	if (opt->progress)
 		strvec_pushf(&rev_list.args, "--progress=%s",
 			     _("Checking connectivity"));
diff --git a/odb.c b/odb.c
index 7d555be09feaea..e431bcb84c80ed 100644
--- a/odb.c
+++ b/odb.c
@@ -453,6 +453,17 @@ static int refs_from_alternate_cb(struct odb_source *alternate,
 		goto out;
 	strbuf_setlen(&path, base_len);
 
+	/* A shallow or grafted repository may lack the history behind its refs. */
+	strbuf_addstr(&path, "/shallow");
+	if (!access(path.buf, F_OK))
+		goto out;
+	strbuf_setlen(&path, base_len);
+
+	strbuf_addstr(&path, "/info/grafts");
+	if (!access(path.buf, F_OK))
+		goto out;
+	strbuf_setlen(&path, base_len);
+
 	read_alternate_refs(alternate->odb->repo, path.buf, cb->fn, cb->payload);
 
 out:
diff --git a/t/t5618-alternate-refs.sh b/t/t5618-alternate-refs.sh
index 2fb6d549d394ee..9c3862709a6d08 100755
--- a/t/t5618-alternate-refs.sh
+++ b/t/t5618-alternate-refs.sh
@@ -58,4 +58,29 @@ test_expect_success 'log --source shows .alternate marker' '
 	test_cmp expect actual
 '
 
+test_expect_success 'connectivity check of a fetch excludes alternate refs' '
+	GIT_TRACE2_EVENT="$PWD/fetch.trace" git fetch origin &&
+	test_subcommand_flex git rev-list --objects --stdin --not --all \
+		--alternate-refs --quiet <fetch.trace
+'
+
+test_expect_success 'connectivity check of a deepening fetch excludes alternate refs' '
+	GIT_TRACE2_EVENT="$PWD/deepen.trace" git fetch --depth=1 origin one &&
+	test_subcommand_flex git rev-list --objects --stdin --not \
+		--alternate-refs --quiet <deepen.trace
+'
+
+test_expect_success 'refs of a shallow alternate are ignored' '
+	git clone --depth=1 "file://$TRASH_DIRECTORY" "$TRASH_DIRECTORY/shallow" &&
+	test_commit -C "$TRASH_DIRECTORY/shallow" shallow-only &&
+	git -C "$TRASH_DIRECTORY/shallow" rev-parse HEAD >shallow-tip &&
+	cp .git/objects/info/alternates alternates.bak &&
+	test_when_finished "mv alternates.bak .git/objects/info/alternates" &&
+	echo "$TRASH_DIRECTORY/shallow/.git/objects" >>.git/objects/info/alternates &&
+	git cat-file -e $(cat shallow-tip) &&
+	git rev-list --remotes=origin >expect &&
+	git rev-list --alternate-refs >actual &&
+	test_cmp expect actual
+'
+
 test_done