How do I pound chicken (or other meat) without making a mess? Despite my best efforts, my kitchen (and sometimes the chicken) always looks like a war zone after pounding 8 or 10 breasts.  Maybe this is just a messy job, but I think there must be something I'm missing.

I've tried using mallets, both metal and wooden  The meat always gets stuck to the pounding surface and the mallet.  I've tried putting the meat inside a plastic sandwich bag or freezer bag; the bag is always ripping and falling apart before the meat is flat.  Wax paper is about the same.

I've also tried rolling pins.  Even got a "non-stick" one.  This way is even more hopeless for me, because the meat either slides around on the surface or sticks to the pin (doesn't matter if I use flour).

Surely there must be a combination of tools and techniques that would allow me to complete this task without requiring 20 minutes of constant cursing and an extra hour of cleanup.

Can anyone point me in the right direction?
Clingwrap works fine for me -- but I don't use a meat tenderizer -- I just use a small but fairly heavy pan (but not my cast iron, as it's not smooth on the bottom).

When I was in college, I tried a few things.  I can get pretty decent results just hitting it with my cutting board.  (with it between saran wrap).

Part of it might be technique -- if I'm doing chicken breast I first slice is sort of following the taper of the breast, so it's neither with or across the grain, but kinda of diagonal.  You also don't want to hit straight down -- you want to angle the blows, so you're actually pushing the meat out, and not just trying to force it through the counter.

And I should mention that I've only ever pounded out poultry and pork -- I assume beef would be the same, but I have no experience to confirm or deny it.