The problem of presupposition projection is the problem of relating the presuppositions of complex sentences to the presuppositions of their parts, in an application of the general principle of semantic compositionality. It has been agreed, ever since Karttunen's papers on the subject in the 1970s, that sentences do inherit the presuppositions of their parts, i.e. that presuppositions do project, but under certain quite complex conditions. But what is the form of the projection? This seems to depend on the form of the sentence. We will look at a specific sentence form that has been much discussed in the literature: conditional sentences that have a presuppositional consequent and a non-presuppositional antecedent (e.g. "if I'm not tired then I'll take my dog for a long walk", where "my dog" presupposes that I have a dog). Some theories (e.g. Update Semantics) argue that in these sorts of sentences the presupposition always gets conditionalized as it projects. Update Semantics has been very successful. But it has not been able to account for the quite persuasive intuition that some projections seem conditional and some not. To explain this intuition, it is generally claimed that under certain circumstances the projection gets strengthened (i.e. non-conditionalized). However, there is no consensus yet on just what these circumstances are. I will argue that, in a sense, we are dealing with a non-problem, i.e. that the intuition that projections are conditionalized should not be taken at face value. What appears to be a conditionalized projection is actually a conditional entailment of the sentence, produced by an interaction effect between presupposition and implicature, among other types of reasoning. In other words, I will argue that if we are careful to disentangle different sorts of reasoning processes, we can see a way to solve the projection problem, by seeing that it never really existed.