The Principle of Sufficient Reason (PSR) says that, necessarily, every contingently true proposition has an explanation. The PSR is the most controversial premise in the cosmological argument for the existence of God. It is likely that one reason why a number of philosophers reject the PSR is that they think there are conceptual counter-examples to it. For instance, they may think, with Peter van Inwagen, that the conjunction of all contingent propositions cannot have an explanation, or they may believe that quantum mechanical phenomena cannot be explained. It may, however, be that these philosophers would be open to accepting a restricted version of the PSR as long as it was not ad hoc. I present a natural restricted version of the PSR that avoids all conceptual counter-examples, and yet that is strong enough to ground a cosmological argument. The restricted PSR says that all explainable true propositions have explanations.