Random numbers with specific sum and varying maximum

How can I generate random numbers with a specific sum and a specific minimum (zero) but varying maximum? I already tried randfixedsum function but the maximum is fixed not varying.

Answer 1

[Jeff Miller]

How about first picking the maximum "thismax" randomly from whatever distribution you want, and then using randfixedsum to generate the remainder "desired_total-thismax" the remaining n-1 numbers?