Not avoiding booze quite a target (4)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

PRE [tt] Y (quite, as in pretty well = quite well = reasonably well), without TT (abbreviation for teetotal = avoiding booze). My last one in by a very long way: I could guess the definition from the crossers, but the wordplay almost defeated me. Prey = target = an animal that is typically eaten by a larger one.