help with formula to calculate cell location

i'm not sure how to describe this. i've never had to do this before.

here is what i'm trying to do. and it's not working.

=MIN(B2:B(G2-G3))

basically instead of saying =MIN(B2:Bx)....i want the "x" to be variable based upong the G2-G3 condition. can this be done some other way?

thanks
adam