We formally show that sequential reasoning is adequate and sufficient for establishing soundness of various optimizations in compilers targeting weakly consistent shared-memory concurrency. Concretely, we introduce a sequential model and show that behavioral refinement in that model entails contextual refinement in the Promising Semantics model, extended with non-atomic accesses for non-racy code. This is the first work to achieve such result for a full-fledged model with a variety of C11-style concurrency features, and the first to lift the data-race-freedom assumption, thus validating irrelevant load introduction, which is commonly performed by compilers. Then, by relying solely on the sequential model, we develop a certified optimizer (in Coq) for a toy concurrent language. We believe that our approach provides useful means for compiler developers and validators, and a solid foundation for the development of certified optimizing compilers for weakly consistent shared-memory concurrency.