diff --git a/autoload/fugitive.vim b/autoload/fugitive.vim
index 880ef23..08292b1 100644
--- a/autoload/fugitive.vim
+++ b/autoload/fugitive.vim
@@ -821,12 +821,19 @@ function! fugitive#writefile(lines, url, ...) abort
   return call('writefile', [a:lines, a:url] + a:000)
 endfunction
 
-let s:globsubs = {'*': '[^/]*', '**': '.*', '**/': '\%(.*/\)\=', '?': '[^/]'}
+let s:globsubs = {
+      \ '/**/': '/\%([^./][^/]*/\)*',
+      \ '/**': '/\%([^./][^/]\+/\)*[^./][^/]*',
+      \ '**/': '[^/]*\%(/[^./][^/]*\)*',
+      \ '**': '.*',
+      \ '/*': '/[^/.][^/]*',
+      \ '*': '[^/]*',
+      \ '?': '[^/]'}
 function! fugitive#glob(url, ...) abort
   let [dirglob, commit, glob] = s:DirCommitFile(a:url)
   let append = matchstr(glob, '/*$')
   let glob = substitute(glob, '/*$', '', '')
-  let pattern = '^' . substitute(glob[1:-1], '\*\*/\=\|[.?*\^$]', '\=get(s:globsubs, submatch(0), "\\" . submatch(0))', 'g') . '$'
+  let pattern = '^' . substitute(glob, '/\=\*\*/\=\|/\=\*\|[.?\^$]', '\=get(s:globsubs, submatch(0), "\\" . submatch(0))', 'g')[1:-1] . '$'
   let results = []
   for dir in dirglob =~# '[*?]' ? split(glob(dirglob), "\n") : [dirglob]
     if empty(dir) || !get(g:, 'fugitive_file_api', 1) || !filereadable(dir . '/HEAD')