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I have to throw in a vote for Jagged Mountain. And add my plus one for these two beauties:

Coxcomb is in my top 3 favorite 13er climbs to date, if not my single favorite. Solid, sustained class 3/4 chimney leading to a narrow summit ridge, a rap into a notch which you then top rope on the return (class 5), finished off by a long, fun rappel with great views of the Cimarrons, Wetterhorn, and Uncompahgre throughout. The entire outing encompasses a little bit of everything I find fun about summer hiking/climbing, and definitely meets your criteria for class 3, 4, and 5. A pic taken along the summit ridge (from our TR):

That sounds incredible. Adding it to my list.

+1 for Coxcomb. By far my favorite climb to date.