OP stated that the crank he is interested in recommends a 110 or 113MM BB.
OP has a "mid 80's TREK".

Unless the frame has been re-spaced, it has a 126MM drop outs.
The 113MM is what one would recommend for a "modern" 135MM spaced frame.
The 110MM is what one would recommend for a 130MM Road Bike spacing.
ERGO, he needs the shorter BB. More likely a 108mm, but 110 should work.

I just went through the SAME thing, installing a NEW crank & BB on my 86 RockHopper With same BB length recommendations (110 & 113) for the crank.
I chose the 110MM and it's about 2MM long.

That works for me, since I tend to use the outer cogs more than normal.