Heh, I don't know why I didn't even realize it right away -- that the valves would be just as thick as a trumpet's!
Well at least this is easier to fix than spending precious money on buying a smaller instrument just for that reason.
And yes, my trumpet is equipped with an adjustable 3rd valve ring that can be replaced with a lyre during marching season. =) It's just a student Yamaha, but other than it's cumbersome weight, it's not too shabby.
Thanks for the help, everyone.