Adapted neosnippets source. Examples by petobens.

autoload/neocomplete/sources/ultisnips.vim

@@ -4,12 +4,27 @@ set cpo&vim
 let s:source = {
    \ 'name' : 'ultisnips',
    \ 'kind' : 'keyword',
+   \ 'mark' : '[US]',
    \ 'rank' : 8,
-      \ 'mark' : '[U]',
-      \}
+   \ 'matchers' :
+      \ (g:neocomplete#enable_fuzzy_completion ?
+      \ ['matcher_fuzzy'] : ['matcher_head']),
+   \ 'min_pattern_length' : 1,
+   \ 'max_candidates' : 20,
+   \ 'is_volatile': 1,
+   \ }
 
 function! s:source.gather_candidates(context)
-  return keys(UltiSnips#SnippetsInCurrentScope())
+   let suggestions = []
+   let snippets = UltiSnips#SnippetsInCurrentScope()
+   for trigger in keys(snippets)
+      let description = get(snippets, trigger)
+      call add(suggestions, {
+         \ 'word' : trigger,
+         \ 'menu' : self.mark . ' '. description
+         \ })
+   endfor
+   return suggestions
 endfunction
 
 function! neocomplete#sources#ultisnips#define()

doc/UltiSnips.txt

@@ -1381,6 +1381,7 @@ individuals have contributed to UltiSnips (in chronological order):
    Gernot Höflechner - LFDM
    Marcelo D Montu - mMontu
    Karl Yngve Lervåg - lervag
+   petobens
 
 Thank you for your support.