  We consider the following conjecture: on a klt germ (X,x), for every finite
set I there is a positive integer N with the property that for every R-ideal J
on X with exponents in I, there is a divisor E over X that computes the minimal
log discrepancy of (X,J) at x and such that its discrepancy k_E is bounded
above by N. We show that this implies Shokurov's ACC conjecture for minimal log
discrepancies on a fixed klt germ and give some partial results towards the
conjecture.
