diff --git a/builtin/clone.c b/builtin/clone.c
index 1e07524c53..e808e02017 100644
--- a/builtin/clone.c
+++ b/builtin/clone.c
@@ -970,7 +970,7 @@ int cmd_clone(int argc, const char **argv, const char *prefix)
 	int submodule_progress;
 	int filter_submodules = 0;
 	int hash_algo;
-	unsigned int ref_storage_format = REF_STORAGE_FORMAT_UNKNOWN;
+	enum ref_storage_format ref_storage_format = REF_STORAGE_FORMAT_UNKNOWN;
 	const int do_not_override_repo_unix_permissions = -1;
 	const char *template_dir;
 	char *template_dir_dup = NULL;
diff --git a/builtin/init-db.c b/builtin/init-db.c
index 0170469b84..582dcf20f8 100644
--- a/builtin/init-db.c
+++ b/builtin/init-db.c
@@ -81,7 +81,7 @@ int cmd_init_db(int argc, const char **argv, const char *prefix)
 	const char *ref_format = NULL;
 	const char *initial_branch = NULL;
 	int hash_algo = GIT_HASH_UNKNOWN;
-	unsigned int ref_storage_format = REF_STORAGE_FORMAT_UNKNOWN;
+	enum ref_storage_format ref_storage_format = REF_STORAGE_FORMAT_UNKNOWN;
 	int init_shared_repository = -1;
 	const struct option init_db_options[] = {
 		OPT_STRING(0, "template", &template_dir, N_("template-directory"),
diff --git a/refs.c b/refs.c
index 31032588e0..e6db85a165 100644
--- a/refs.c
+++ b/refs.c
@@ -37,14 +37,15 @@ static const struct ref_storage_be *refs_backends[] = {
 	[REF_STORAGE_FORMAT_REFTABLE] = &refs_be_reftable,
 };
 
-static const struct ref_storage_be *find_ref_storage_backend(unsigned int ref_storage_format)
+static const struct ref_storage_be *find_ref_storage_backend(
+	enum ref_storage_format ref_storage_format)
 {
 	if (ref_storage_format < ARRAY_SIZE(refs_backends))
 		return refs_backends[ref_storage_format];
 	return NULL;
 }
 
-unsigned int ref_storage_format_by_name(const char *name)
+enum ref_storage_format ref_storage_format_by_name(const char *name)
 {
 	for (unsigned int i = 0; i < ARRAY_SIZE(refs_backends); i++)
 		if (refs_backends[i] && !strcmp(refs_backends[i]->name, name))
@@ -52,7 +53,7 @@ unsigned int ref_storage_format_by_name(const char *name)
 	return REF_STORAGE_FORMAT_UNKNOWN;
 }
 
-const char *ref_storage_format_to_name(unsigned int ref_storage_format)
+const char *ref_storage_format_to_name(enum ref_storage_format ref_storage_format)
 {
 	const struct ref_storage_be *be = find_ref_storage_backend(ref_storage_format);
 	if (!be)
diff --git a/refs.h b/refs.h
index fe7f0db35e..a7afa9bede 100644
--- a/refs.h
+++ b/refs.h
@@ -11,8 +11,14 @@ struct string_list;
 struct string_list_item;
 struct worktree;
 
-unsigned int ref_storage_format_by_name(const char *name);
-const char *ref_storage_format_to_name(unsigned int ref_storage_format);
+enum ref_storage_format {
+	REF_STORAGE_FORMAT_UNKNOWN,
+	REF_STORAGE_FORMAT_FILES,
+	REF_STORAGE_FORMAT_REFTABLE,
+};
+
+enum ref_storage_format ref_storage_format_by_name(const char *name);
+const char *ref_storage_format_to_name(enum ref_storage_format ref_storage_format);
 
 /*
  * Resolve a reference, recursively following symbolic refererences.
diff --git a/repository.c b/repository.c
index d29b0304fb..166863f852 100644
--- a/repository.c
+++ b/repository.c
@@ -124,7 +124,8 @@ void repo_set_compat_hash_algo(struct repository *repo, int algo)
 		repo_read_loose_object_map(repo);
 }
 
-void repo_set_ref_storage_format(struct repository *repo, unsigned int format)
+void repo_set_ref_storage_format(struct repository *repo,
+				 enum ref_storage_format format)
 {
 	repo->ref_storage_format = format;
 }
diff --git a/repository.h b/repository.h
index 4bd8969005..a35cd77c35 100644
--- a/repository.h
+++ b/repository.h
@@ -1,6 +1,7 @@
 #ifndef REPOSITORY_H
 #define REPOSITORY_H
 
+#include "refs.h"
 #include "strmap.h"
 
 struct config_set;
@@ -26,10 +27,6 @@ enum fetch_negotiation_setting {
 	FETCH_NEGOTIATION_NOOP,
 };
 
-#define REF_STORAGE_FORMAT_UNKNOWN  0
-#define REF_STORAGE_FORMAT_FILES    1
-#define REF_STORAGE_FORMAT_REFTABLE 2
-
 struct repo_settings {
 	int initialized;
 
@@ -181,7 +178,7 @@ struct repository {
 	const struct git_hash_algo *compat_hash_algo;
 
 	/* Repository's reference storage format, as serialized on disk. */
-	unsigned int ref_storage_format;
+	enum ref_storage_format ref_storage_format;
 
 	/* A unique-id for tracing purposes. */
 	int trace2_repo_id;
@@ -220,7 +217,8 @@ void repo_set_gitdir(struct repository *repo, const char *root,
 void repo_set_worktree(struct repository *repo, const char *path);
 void repo_set_hash_algo(struct repository *repo, int algo);
 void repo_set_compat_hash_algo(struct repository *repo, int compat_algo);
-void repo_set_ref_storage_format(struct repository *repo, unsigned int format);
+void repo_set_ref_storage_format(struct repository *repo,
+				 enum ref_storage_format format);
 void initialize_repository(struct repository *repo);
 RESULT_MUST_BE_USED
 int repo_init(struct repository *r, const char *gitdir, const char *worktree);
diff --git a/setup.c b/setup.c
index 8c84ec9d4b..b49ee3e95f 100644
--- a/setup.c
+++ b/setup.c
@@ -1997,7 +1997,7 @@ static int needs_work_tree_config(const char *git_dir, const char *work_tree)
 }
 
 void initialize_repository_version(int hash_algo,
-				   unsigned int ref_storage_format,
+				   enum ref_storage_format ref_storage_format,
 				   int reinit)
 {
 	char repo_version_string[10];
@@ -2044,7 +2044,7 @@ static int is_reinit(void)
 	return ret;
 }
 
-void create_reference_database(unsigned int ref_storage_format,
+void create_reference_database(enum ref_storage_format ref_storage_format,
 			       const char *initial_branch, int quiet)
 {
 	struct strbuf err = STRBUF_INIT;
@@ -2243,7 +2243,7 @@ static void validate_hash_algorithm(struct repository_format *repo_fmt, int hash
 }
 
 static void validate_ref_storage_format(struct repository_format *repo_fmt,
-					unsigned int format)
+					enum ref_storage_format format)
 {
 	const char *name = getenv("GIT_DEFAULT_REF_FORMAT");
 
@@ -2263,7 +2263,7 @@ static void validate_ref_storage_format(struct repository_format *repo_fmt,
 
 int init_db(const char *git_dir, const char *real_git_dir,
 	    const char *template_dir, int hash,
-	    unsigned int ref_storage_format,
+	    enum ref_storage_format ref_storage_format,
 	    const char *initial_branch,
 	    int init_shared_repository, unsigned int flags)
 {
diff --git a/setup.h b/setup.h
index b3fd3bf45a..cd8dbc2497 100644
--- a/setup.h
+++ b/setup.h
@@ -1,6 +1,7 @@
 #ifndef SETUP_H
 #define SETUP_H
 
+#include "refs.h"
 #include "string-list.h"
 
 int is_inside_git_dir(void);
@@ -128,7 +129,7 @@ struct repository_format {
 	int is_bare;
 	int hash_algo;
 	int compat_hash_algo;
-	unsigned int ref_storage_format;
+	enum ref_storage_format ref_storage_format;
 	int sparse_index;
 	char *work_tree;
 	struct string_list unknown_extensions;
@@ -192,13 +193,13 @@ const char *get_template_dir(const char *option_template);
 
 int init_db(const char *git_dir, const char *real_git_dir,
 	    const char *template_dir, int hash_algo,
-	    unsigned int ref_storage_format,
+	    enum ref_storage_format ref_storage_format,
 	    const char *initial_branch, int init_shared_repository,
 	    unsigned int flags);
 void initialize_repository_version(int hash_algo,
-				   unsigned int ref_storage_format,
+				   enum ref_storage_format ref_storage_format,
 				   int reinit);
-void create_reference_database(unsigned int ref_storage_format,
+void create_reference_database(enum ref_storage_format ref_storage_format,
 			       const char *initial_branch, int quiet);
 
 /*