Agree with Mman for the most part. People all have their different versions of "top tier." Do you mean top tier clinically? Do you meant top tier research wise? Combination of both?
I always laugh when people say things like Ronin786 ("Wake is a step below in terms of name recognition").... Wake has ZERO problems in name recognition in anesthesia. More than 12 chairs have come from our program. Current editor and chief of Anesthesiology who just won the biggest award at the ASA and was elected to the Institute of Medicine. Oh, and we won the biggest service award at the ASA, too. On top of that, I can assure you that the clinical training you get at Wake is just as good or better than every program on that list. There's a reason we match as highly as we do, and it's not because people love Winston (though, I honestly do love Winston and find it a great place to train and live and plan on becoming faculty after fellowship)...
If you want a spectacular research experience with a broad based research infrastructure, better can be found at other programs (MGH, Stanford, Brigham, Mayo, etc)... but clinical training at Wake is pretty much second to none. We come out with high acuity, sick patients like any of the top programs. 200-300 blocks, 300 + epidurals including a bunch of thoracic epidurals, 50 + awake fiberoptic intubations, countless more asleep fiberoptic intubations, great peds experiences with a proven track record to match you where you want to go, strong CT experience where fellows don't steal the tough cases because they are doing a boatload of echos (don't sit cases), top 5 pain fellowship, and a neuroanesthesia teaching service that is unparalleled and led by our program director (we aren't even allowed to use Mac or Miller on this rotations, but do we do use a ridiculous amount of lightwands, intubating LMAs, fiberoptic intubations, boullards, retrograde wires, digital intubations, and any other technique you might need in a dire circumstance someday). This is all on top of a structured didactic system (relieved at 3pm to attend lectures daily, though we only have lectures twice per week) that prevents failure.
Oh, and our research infrastructure is improving, too.