diff --git a/builtin/branch.c b/builtin/branch.c
index 2dd51a8653b..8c0b428104d 100644
--- a/builtin/branch.c
+++ b/builtin/branch.c
@@ -740,6 +740,8 @@ int cmd_branch(int argc, const char **argv, const char *prefix)
 		if (!sorting)
 			sorting = ref_default_sorting();
 		ref_sorting_set_sort_flags_all(sorting, REF_SORTING_ICASE, icase);
+		ref_sorting_set_sort_flags_all(
+			sorting, REF_SORTING_DETACHED_HEAD_FIRST, 1);
 		print_ref_list(&filter, sorting, &format);
 		print_columns(&output, colopts, NULL);
 		string_list_clear(&output, 0);
diff --git a/ref-filter.c b/ref-filter.c
index fe587afb80b..8d0739b9972 100644
--- a/ref-filter.c
+++ b/ref-filter.c
@@ -1536,36 +1536,27 @@ char *get_head_description(void)
 	struct wt_status_state state;
 	memset(&state, 0, sizeof(state));
 	wt_status_get_state(the_repository, &state, 1);
-
-	/*
-	 * The ( character must be hard-coded and not part of a localizable
-	 * string, since the description is used as a sort key and compared
-	 * with ref names.
-	 */
-	strbuf_addch(&desc, '(');
 	if (state.rebase_in_progress ||
 	    state.rebase_interactive_in_progress) {
 		if (state.branch)
-			strbuf_addf(&desc, _("no branch, rebasing %s"),
+			strbuf_addf(&desc, _("(no branch, rebasing %s)"),
 				    state.branch);
 		else
-			strbuf_addf(&desc, _("no branch, rebasing detached HEAD %s"),
+			strbuf_addf(&desc, _("(no branch, rebasing detached HEAD %s)"),
 				    state.detached_from);
 	} else if (state.bisect_in_progress)
-		strbuf_addf(&desc, _("no branch, bisect started on %s"),
+		strbuf_addf(&desc, _("(no branch, bisect started on %s)"),
 			    state.branch);
 	else if (state.detached_from) {
 		if (state.detached_at)
-			strbuf_addstr(&desc, HEAD_DETACHED_AT);
+			strbuf_addf(&desc, _("(HEAD detached at %s)"),
+				state.detached_from);
 		else
-			strbuf_addstr(&desc, HEAD_DETACHED_FROM);
-		strbuf_addstr(&desc, state.detached_from);
-	}
-	else
-		strbuf_addstr(&desc, _("no branch"));
-	strbuf_addch(&desc, ')');
+			strbuf_addf(&desc, _("(HEAD detached from %s)"),
+				state.detached_from);
+	} else
+		strbuf_addstr(&desc, _("(no branch)"));
 
-	wt_status_state_free_buffers(&state);
 	return strbuf_detach(&desc, NULL);
 }
 
@@ -2350,6 +2341,18 @@ int filter_refs(struct ref_array *array, struct ref_filter *filter, unsigned int
 	return ret;
 }
 
+static int compare_detached_head(struct ref_array_item *a, struct ref_array_item *b)
+{
+	if (!(a->kind ^ b->kind))
+		BUG("ref_kind_from_refname() should only mark one ref as HEAD");
+	if (a->kind & FILTER_REFS_DETACHED_HEAD)
+		return -1;
+	else if (b->kind & FILTER_REFS_DETACHED_HEAD)
+		return 1;
+	BUG("should have died in the xor check above");
+	return 0;
+}
+
 static int cmp_ref_sorting(struct ref_sorting *s, struct ref_array_item *a, struct ref_array_item *b)
 {
 	struct atom_value *va, *vb;
@@ -2362,7 +2365,10 @@ static int cmp_ref_sorting(struct ref_sorting *s, struct ref_array_item *a, stru
 	if (get_ref_atom_value(b, s->atom, &vb, &err))
 		die("%s", err.buf);
 	strbuf_release(&err);
-	if (s->sort_flags & REF_SORTING_VERSION) {
+	if (s->sort_flags & REF_SORTING_DETACHED_HEAD_FIRST &&
+	    ((a->kind | b->kind) & FILTER_REFS_DETACHED_HEAD)) {
+		cmp = compare_detached_head(a, b);
+	} else if (s->sort_flags & REF_SORTING_VERSION) {
 		cmp = versioncmp(va->s, vb->s);
 	} else if (cmp_type == FIELD_STR) {
 		int (*cmp_fn)(const char *, const char *);
diff --git a/ref-filter.h b/ref-filter.h
index 6296ae8bb27..19ea4c41340 100644
--- a/ref-filter.h
+++ b/ref-filter.h
@@ -32,6 +32,7 @@ struct ref_sorting {
 		REF_SORTING_REVERSE = 1<<0,
 		REF_SORTING_ICASE = 1<<1,
 		REF_SORTING_VERSION = 1<<2,
+		REF_SORTING_DETACHED_HEAD_FIRST = 1<<3,
 	} sort_flags;
 };
 
diff --git a/t/t3203-branch-output.sh b/t/t3203-branch-output.sh
index f92fb3aab9d..8f53b081365 100755
--- a/t/t3203-branch-output.sh
+++ b/t/t3203-branch-output.sh
@@ -223,8 +223,8 @@ test_expect_success 'git branch `--sort=[-]objectsize` option' '
 	cat >expect <<-\EOF &&
 	  branch-one
 	  main
-	* (HEAD detached from fromtag)
 	  branch-two
+	* (HEAD detached from fromtag)
 	EOF
 	git branch --sort=-objectsize >actual &&
 	test_i18ncmp expect actual
@@ -241,10 +241,10 @@ test_expect_success 'git branch `--sort=[-]type` option' '
 	test_i18ncmp expect actual &&
 
 	cat >expect <<-\EOF &&
-	* (HEAD detached from fromtag)
 	  branch-one
 	  branch-two
 	  main
+	* (HEAD detached from fromtag)
 	EOF
 	git branch --sort=-type >actual &&
 	test_i18ncmp expect actual
diff --git a/wt-status.c b/wt-status.c
index 7074bbdd53c..40b59be478c 100644
--- a/wt-status.c
+++ b/wt-status.c
@@ -1742,9 +1742,9 @@ static void wt_longstatus_print(struct wt_status *s)
 			} else if (s->state.detached_from) {
 				branch_name = s->state.detached_from;
 				if (s->state.detached_at)
-					on_what = HEAD_DETACHED_AT;
+					on_what = _("HEAD detached at ");
 				else
-					on_what = HEAD_DETACHED_FROM;
+					on_what = _("HEAD detached from ");
 			} else {
 				branch_name = "";
 				on_what = _("Not currently on any branch.");
diff --git a/wt-status.h b/wt-status.h
index 35b44c388ed..0d32799b28e 100644
--- a/wt-status.h
+++ b/wt-status.h
@@ -77,8 +77,6 @@ enum wt_status_format {
 	STATUS_FORMAT_UNSPECIFIED
 };
 
-#define HEAD_DETACHED_AT _("HEAD detached at ")
-#define HEAD_DETACHED_FROM _("HEAD detached from ")
 #define SPARSE_CHECKOUT_DISABLED -1
 
 struct wt_status_state {