I've shot Remington Sub-sonics on grouse (head shots only) and rabbits. They've done just fine on either one. They're as accurate as Remington Target or Federal standard velocity out of my Anschutz 64 or Remington 541 and have fewer fliers than the Remington Target. They also used to be pretty inexpensive.

I bought a carton of the Winchester sub-sonics but haven't had a chance to get out to the range and see how they do.