Pass through is my biggest issue on most shots at starlings or pigeons (30 yrds and usually much less). As such, HP's are my pellet of choice, though I think the CPHP's are a bit too hard and round. I really like the Crow Mags, or the Silver Bears. Bear in mind that I'm using a Big Cat so they're coming out pretty hot.
On the other hand, if accuracy is your biggest issue and/or you aren't shooting so fast, I'd focus on a pellet that's consistently accurate, which is probably going to be a better quality domed pellet.