There's little in the frequent flyer world that I'm an expert in, but this is one subject I know a thing or two about.

The most important and meaningful advice here has already been given: "If you want to make sure they won't make you valet check it, you are better off with a non-wheeled bag, such as a backpack or duffel." And note that "better off" is something of an understatement.

The second bit of advice is this. The governing dimension here is the width (thickness) of the bag since the bin opening is just eight inches -- and even then your bag had better be soft. See the prior paragraph.

Third, and contrary to what's said above, "valet" checking absolutely, positively does NOT invariably mean that you get to pick your stuff up planeside upon arrival. In some places you sometimes end up at the carrousel no matter what. Not often but sometimes. My memory may be faulty, but I believe the last time this happened for one of my flights was on a UA ALB-ORD flight about a year or so ago. Of course, I hadn't checked anything and so I didn't care.

Finally, don't be in one of the last two boarding groups. On some airlines, they just say, "If you're in group 3 or higher, you have to check," or something similar. So that, in case you're wondering, is why there's such a thing as co-branded credit cards. "Some airlines," I should confess, is a euphemism for UA.