Many theists and atheists believe that God would not permit an evil unless God’s allowing it (or an evil at least as bad) is required for a greater good. In “The Argument from Particular Horrendous Evils” (and elsewhere) Peter van Inwagen has argued against this belief by appealing to his “No Minimum Claim” (NMC), namely, that it is reasonable to believe there is no minimum amount of evil required for God’s purposes. In this paper I distinguish different formulations of NMC, (...) and, by drawing an instructive parallel to traditional sorites paradoxes, refute Jeff Jordan’s criticism that because morally significant suffering is finitelydiminishable, NMC must be false. (shrink)