In this talk, I will discuss two new problems for the satisfaction theory of presupposition. In 1996 Bart Geurts pointed out that a certain impossibility predicted by the satisfaction theory of presupposition was not borne out; he called this the Proviso Problem. Where the theory predicted that there could be no atomic, or logically strong presuppositions of conditional sentences, Geurts found that in many very natural cases, the presupposition projected is just the strong one. For example, "If John is not tired he'll read his Bible tonight" does not intuitively presuppose that "If John is not tired he has a Bible", but rather "John has a Bible". A crack was thus discovered in the compositional theory of presupposition that the satisfaction theory delivers. Attempts were soon made (and are ongoing) to close the crack; people argued for a two-stage account wherein under some circumstances, after semantics has done its work, pragmatic processes enter to restrengthen the predicted presupposition (to yield, e.g., "John has a Bible", in the case above.). We will see two new problems with the satisfaction theory that no amount of strengthening can fix; both problems show that certain impossibility predictions that satisfaction + strengthening make are not borne out (hence the nod to Geurts in the title). The first impossibility prediction is that a sentence cannot have both weak and strong presuppositions, and the second that there can be no weak presuppositions without any strong (i.e. without any explicit presupposition triggers). I will discuss a projection algorithm that predicts the correct presuppositions in all the classic cases, as well as those uncovered by the strengthening papers, and my new cases also. If there is time, I will discuss some big-picture consequences of this new algorithm, among which are that presupposition computations are noncompositional, and that nonmonotonicity (familiar from AI) enters into the theory of pragmatic competence (rather than being an artifact of human performance limitations).