(partial?) indexes, LIKE and NULL

Hi,

with the following table:

     Table "public.foo"
  Column | Type | Modifiers
--------+------+-----------
  t      | text |
Indexes:
      "a" btree (t)

Shouldn't queries that use
    ... where t like '%something%'

benefit from "a" when t is NULL in almost all cases, since the query
planner could use "a" to access the few non-NULL rows quickly? It
doesn't seem to work right now.

(I assume that it would make no difference if the index "a" was partial,
excluding NULLs)

Regards,
-mjy