diff --git a/refs/files-backend.c b/refs/files-backend.c
index 88f8c7aa4b..bce0022345 100644
--- a/refs/files-backend.c
+++ b/refs/files-backend.c
@@ -2280,10 +2280,18 @@ static int pack_if_possible_fn(struct ref_entry *entry, void *cb_data)
 	return 0;
 }
 
+enum {
+	REMOVE_EMPTY_PARENTS_REF = 0x01,
+	REMOVE_EMPTY_PARENTS_REFLOG = 0x02
+};
+
 /*
- * Remove empty parents, but spare refs/ and immediate subdirs.
+ * Remove empty parent directories associated with the specified
+ * reference and/or its reflog, but spare [logs/]refs/ and immediate
+ * subdirs. flags is a combination of REMOVE_EMPTY_PARENTS_REF and/or
+ * REMOVE_EMPTY_PARENTS_REFLOG.
  */
-static void try_remove_empty_parents(const char *refname)
+static void try_remove_empty_parents(const char *refname, unsigned int flags)
 {
 	struct strbuf buf = STRBUF_INIT;
 	char *p, *q;
@@ -2299,7 +2307,7 @@ static void try_remove_empty_parents(const char *refname)
 			p++;
 	}
 	q = buf.buf + buf.len;
-	while (1) {
+	while (flags & (REMOVE_EMPTY_PARENTS_REF | REMOVE_EMPTY_PARENTS_REFLOG)) {
 		while (q > p && *q != '/')
 			q--;
 		while (q > p && *(q-1) == '/')
@@ -2307,8 +2315,12 @@ static void try_remove_empty_parents(const char *refname)
 		if (q == p)
 			break;
 		strbuf_setlen(&buf, q - buf.buf);
-		if (rmdir(git_path("%s", buf.buf)))
-			break;
+		if ((flags & REMOVE_EMPTY_PARENTS_REF) &&
+		    rmdir(git_path("%s", buf.buf)))
+			flags &= ~REMOVE_EMPTY_PARENTS_REF;
+		if ((flags & REMOVE_EMPTY_PARENTS_REFLOG) &&
+		    rmdir(git_path("logs/%s", buf.buf)))
+			flags &= ~REMOVE_EMPTY_PARENTS_REFLOG;
 	}
 	strbuf_release(&buf);
 }
@@ -2334,7 +2346,7 @@ static void prune_ref(struct ref_to_prune *r)
 	}
 	ref_transaction_free(transaction);
 	strbuf_release(&err);
-	try_remove_empty_parents(r->name);
+	try_remove_empty_parents(r->name, REMOVE_EMPTY_PARENTS_REF);
 }
 
 static void prune_refs(struct ref_to_prune *r)