diff --git a/setup.c b/setup.c
index 25a3038277..e2a479a64f 100644
--- a/setup.c
+++ b/setup.c
@@ -798,7 +798,7 @@ static const char *setup_discovered_git_dir(const char *gitdir,
 		set_git_dir(gitdir);
 	inside_git_dir = 0;
 	inside_work_tree = 1;
-	if (offset == cwd->len)
+	if (offset >= cwd->len)
 		return NULL;
 
 	/* Make "offset" point past the '/' (already the case for root dirs) */
@@ -920,7 +920,7 @@ static enum discovery_result setup_git_directory_gently_1(struct strbuf *dir,
 	const char *env_ceiling_dirs = getenv(CEILING_DIRECTORIES_ENVIRONMENT);
 	struct string_list ceiling_dirs = STRING_LIST_INIT_DUP;
 	const char *gitdirenv;
-	int ceil_offset = -1, min_offset = has_dos_drive_prefix(dir->buf) ? 3 : 1;
+	int ceil_offset = -1, min_offset = offset_1st_component(dir->buf);
 	dev_t current_device = 0;
 	int one_filesystem = 1;
 
@@ -948,6 +948,12 @@ static enum discovery_result setup_git_directory_gently_1(struct strbuf *dir,
 	if (ceil_offset < 0)
 		ceil_offset = min_offset - 2;
 
+	if (min_offset && min_offset == dir->len &&
+	    !is_dir_sep(dir->buf[min_offset - 1])) {
+		strbuf_addch(dir, '/');
+		min_offset++;
+	}
+
 	/*
 	 * Test in the following order (relative to the dir):
 	 * - .git (file containing "gitdir: <path>")