My company doesn't have separate sick days, but you are given 5 days (40 hours) of "personal days" that are independent of your PTO. This seems like a decent compromise in the sense that I can use them as PTO without doing the "pretend to be sick" thing. These do not roll over or accumulate, so they are always the first days of "PTO" used, but they are independent of any tenure or other PTO.