diff --git a/cache.h b/cache.h
index 8e42256942..94475bd9ee 100644
--- a/cache.h
+++ b/cache.h
@@ -737,6 +737,7 @@ int is_directory(const char *);
 const char *real_path(const char *path);
 const char *real_path_if_valid(const char *path);
 const char *absolute_path(const char *path);
+const char *remove_leading_path(const char *in, const char *prefix);
 const char *relative_path(const char *in, const char *prefix, struct strbuf *sb);
 int normalize_path_copy(char *dst, const char *src);
 int longest_ancestor_length(const char *path, struct string_list *prefixes);
diff --git a/path.c b/path.c
index 0c16dc5fdb..fa62da58ed 100644
--- a/path.c
+++ b/path.c
@@ -557,6 +557,51 @@ const char *relative_path(const char *in, const char *prefix,
 	return sb->buf;
 }
 
+/*
+ * A simpler implementation of relative_path
+ *
+ * Get relative path by removing "prefix" from "in". This function
+ * first appears in v1.5.6-1-g044bbbc, and makes git_dir shorter
+ * to increase performance when traversing the path to work_tree.
+ */
+const char *remove_leading_path(const char *in, const char *prefix)
+{
+	static char buf[PATH_MAX + 1];
+	int i = 0, j = 0;
+
+	if (!prefix || !prefix[0])
+		return in;
+	while (prefix[i]) {
+		if (is_dir_sep(prefix[i])) {
+			if (!is_dir_sep(in[j]))
+				return in;
+			while (is_dir_sep(prefix[i]))
+				i++;
+			while (is_dir_sep(in[j]))
+				j++;
+			continue;
+		} else if (in[j] != prefix[i]) {
+			return in;
+		}
+		i++;
+		j++;
+	}
+	if (
+	    /* "/foo" is a prefix of "/foo" */
+	    in[j] &&
+	    /* "/foo" is not a prefix of "/foobar" */
+	    !is_dir_sep(prefix[i-1]) && !is_dir_sep(in[j])
+	   )
+		return in;
+	while (is_dir_sep(in[j]))
+		j++;
+	if (!in[j])
+		strcpy(buf, ".");
+	else
+		strcpy(buf, in + j);
+	return buf;
+}
+
 /*
  * It is okay if dst == src, but they should not overlap otherwise.
  *
diff --git a/setup.c b/setup.c
index 0d9ea6239f..dad39c1aba 100644
--- a/setup.c
+++ b/setup.c
@@ -360,7 +360,6 @@ int is_inside_work_tree(void)
 
 void setup_work_tree(void)
 {
-	struct strbuf sb = STRBUF_INIT;
 	const char *work_tree, *git_dir;
 	static int initialized = 0;
 
@@ -380,10 +379,8 @@ void setup_work_tree(void)
 	if (getenv(GIT_WORK_TREE_ENVIRONMENT))
 		setenv(GIT_WORK_TREE_ENVIRONMENT, ".", 1);
 
-	set_git_dir(relative_path(git_dir, work_tree, &sb));
+	set_git_dir(remove_leading_path(git_dir, work_tree));
 	initialized = 1;
-
-	strbuf_release(&sb);
 }
 
 static int check_repository_format_gently(const char *gitdir, int *nongit_ok)