diff --git a/builtin/branch.c b/builtin/branch.c
index 9b68591addf..8c0b428104d 100644
--- a/builtin/branch.c
+++ b/builtin/branch.c
@@ -726,7 +726,7 @@ int cmd_branch(int argc, const char **argv, const char *prefix)
 		print_current_branch_name();
 		return 0;
 	} else if (list) {
-		/*  git branch --local also shows HEAD when it is detached */
+		/*  git branch --list also shows HEAD when it is detached */
 		if ((filter.kind & FILTER_REFS_BRANCHES) && filter.detached)
 			filter.kind |= FILTER_REFS_DETACHED_HEAD;
 		filter.name_patterns = argv;
@@ -739,7 +739,9 @@ int cmd_branch(int argc, const char **argv, const char *prefix)
 		 */
 		if (!sorting)
 			sorting = ref_default_sorting();
-		ref_sorting_icase_all(sorting, icase);
+		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/builtin/for-each-ref.c b/builtin/for-each-ref.c
index 9d1ecda2b8f..cb9c81a0460 100644
--- a/builtin/for-each-ref.c
+++ b/builtin/for-each-ref.c
@@ -70,7 +70,7 @@ int cmd_for_each_ref(int argc, const char **argv, const char *prefix)
 
 	if (!sorting)
 		sorting = ref_default_sorting();
-	ref_sorting_icase_all(sorting, icase);
+	ref_sorting_set_sort_flags_all(sorting, REF_SORTING_ICASE, icase);
 	filter.ignore_case = icase;
 
 	filter.name_patterns = argv;
diff --git a/builtin/tag.c b/builtin/tag.c
index ecf011776dc..24d35b746d1 100644
--- a/builtin/tag.c
+++ b/builtin/tag.c
@@ -485,7 +485,7 @@ int cmd_tag(int argc, const char **argv, const char *prefix)
 	}
 	if (!sorting)
 		sorting = ref_default_sorting();
-	ref_sorting_icase_all(sorting, icase);
+	ref_sorting_set_sort_flags_all(sorting, REF_SORTING_ICASE, icase);
 	filter.ignore_case = icase;
 	if (cmdmode == 'l') {
 		int ret;
diff --git a/ref-filter.c b/ref-filter.c
index aa260bfd099..ee337df232a 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);
 }
 
@@ -2350,12 +2341,24 @@ 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;
 	int cmp;
+	int cmp_detached_head = 0;
 	cmp_type cmp_type = used_atom[s->atom].type;
-	int (*cmp_fn)(const char *, const char *);
 	struct strbuf err = STRBUF_INIT;
 
 	if (get_ref_atom_value(a, s->atom, &va, &err))
@@ -2363,12 +2366,18 @@ 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);
-	cmp_fn = s->ignore_case ? strcasecmp : strcmp;
-	if (s->version)
+	if (s->sort_flags & REF_SORTING_DETACHED_HEAD_FIRST &&
+	    ((a->kind | b->kind) & FILTER_REFS_DETACHED_HEAD)) {
+		cmp = compare_detached_head(a, b);
+		cmp_detached_head = 1;
+	} else if (s->sort_flags & REF_SORTING_VERSION) {
 		cmp = versioncmp(va->s, vb->s);
-	else if (cmp_type == FIELD_STR)
+	} else if (cmp_type == FIELD_STR) {
+		int (*cmp_fn)(const char *, const char *);
+		cmp_fn = s->sort_flags & REF_SORTING_ICASE
+			? strcasecmp : strcmp;
 		cmp = cmp_fn(va->s, vb->s);
-	else {
+	} else {
 		if (va->value < vb->value)
 			cmp = -1;
 		else if (va->value == vb->value)
@@ -2377,7 +2386,8 @@ static int cmp_ref_sorting(struct ref_sorting *s, struct ref_array_item *a, stru
 			cmp = 1;
 	}
 
-	return (s->reverse) ? -cmp : cmp;
+	return (s->sort_flags & REF_SORTING_REVERSE && !cmp_detached_head)
+		? -cmp : cmp;
 }
 
 static int compare_refs(const void *a_, const void *b_, void *ref_sorting)
@@ -2392,15 +2402,20 @@ static int compare_refs(const void *a_, const void *b_, void *ref_sorting)
 			return cmp;
 	}
 	s = ref_sorting;
-	return s && s->ignore_case ?
+	return s && s->sort_flags & REF_SORTING_ICASE ?
 		strcasecmp(a->refname, b->refname) :
 		strcmp(a->refname, b->refname);
 }
 
-void ref_sorting_icase_all(struct ref_sorting *sorting, int flag)
+void ref_sorting_set_sort_flags_all(struct ref_sorting *sorting,
+				    unsigned int mask, int on)
 {
-	for (; sorting; sorting = sorting->next)
-		sorting->ignore_case = !!flag;
+	for (; sorting; sorting = sorting->next) {
+		if (on)
+			sorting->sort_flags |= mask;
+		else
+			sorting->sort_flags &= ~mask;
+	}
 }
 
 void ref_array_sort(struct ref_sorting *sorting, struct ref_array *array)
@@ -2537,12 +2552,12 @@ void parse_ref_sorting(struct ref_sorting **sorting_tail, const char *arg)
 	*sorting_tail = s;
 
 	if (*arg == '-') {
-		s->reverse = 1;
+		s->sort_flags |= REF_SORTING_REVERSE;
 		arg++;
 	}
 	if (skip_prefix(arg, "version:", &arg) ||
 	    skip_prefix(arg, "v:", &arg))
-		s->version = 1;
+		s->sort_flags |= REF_SORTING_VERSION;
 	s->atom = parse_sorting_atom(arg);
 }
 
diff --git a/ref-filter.h b/ref-filter.h
index feaef4a8fde..19ea4c41340 100644
--- a/ref-filter.h
+++ b/ref-filter.h
@@ -28,9 +28,12 @@ struct atom_value;
 struct ref_sorting {
 	struct ref_sorting *next;
 	int atom; /* index into used_atom array (internal) */
-	unsigned reverse : 1,
-		ignore_case : 1,
-		version : 1;
+	enum {
+		REF_SORTING_REVERSE = 1<<0,
+		REF_SORTING_ICASE = 1<<1,
+		REF_SORTING_VERSION = 1<<2,
+		REF_SORTING_DETACHED_HEAD_FIRST = 1<<3,
+	} sort_flags;
 };
 
 struct ref_array_item {
@@ -109,8 +112,8 @@ void ref_array_clear(struct ref_array *array);
 int verify_ref_format(struct ref_format *format);
 /*  Sort the given ref_array as per the ref_sorting provided */
 void ref_array_sort(struct ref_sorting *sort, struct ref_array *array);
-/*  Set the ignore_case flag for all elements of a sorting list */
-void ref_sorting_icase_all(struct ref_sorting *sorting, int flag);
+/*  Set REF_SORTING_* sort_flags for all elements of a sorting list */
+void ref_sorting_set_sort_flags_all(struct ref_sorting *sorting, unsigned int mask, int on);
 /*  Based on the given format and quote_style, fill the strbuf */
 int format_ref_array_item(struct ref_array_item *info,
 			  const struct ref_format *format,
diff --git a/t/t3203-branch-output.sh b/t/t3203-branch-output.sh
index b945faf4702..5e0577d5c7f 100755
--- a/t/t3203-branch-output.sh
+++ b/t/t3203-branch-output.sh
@@ -210,7 +210,7 @@ EOF
 	test_i18ncmp expect actual
 '
 
-test_expect_success 'git branch `--sort` option' '
+test_expect_success 'git branch `--sort=[-]objectsize` option' '
 	cat >expect <<-\EOF &&
 	* (HEAD detached from fromtag)
 	  branch-two
@@ -218,6 +218,55 @@ test_expect_success 'git branch `--sort` option' '
 	  main
 	EOF
 	git branch --sort=objectsize >actual &&
+	test_i18ncmp expect actual &&
+
+	cat >expect <<-\EOF &&
+	* (HEAD detached from fromtag)
+	  branch-one
+	  main
+	  branch-two
+	EOF
+	git branch --sort=-objectsize >actual &&
+	test_i18ncmp expect actual
+'
+
+test_expect_success 'git branch `--sort=[-]type` option' '
+	cat >expect <<-\EOF &&
+	* (HEAD detached from fromtag)
+	  branch-one
+	  branch-two
+	  main
+	EOF
+	git branch --sort=type >actual &&
+	test_i18ncmp expect actual &&
+
+	cat >expect <<-\EOF &&
+	* (HEAD detached from fromtag)
+	  branch-one
+	  branch-two
+	  main
+	EOF
+	git branch --sort=-type >actual &&
+	test_i18ncmp expect actual
+'
+
+test_expect_success 'git branch `--sort=[-]version:refname` option' '
+	cat >expect <<-\EOF &&
+	* (HEAD detached from fromtag)
+	  branch-one
+	  branch-two
+	  main
+	EOF
+	git branch --sort=version:refname >actual &&
+	test_i18ncmp expect actual &&
+
+	cat >expect <<-\EOF &&
+	* (HEAD detached from fromtag)
+	  main
+	  branch-two
+	  branch-one
+	EOF
+	git branch --sort=-version:refname >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 {