What drove inflation so high in 2022? Can it drop rapidly without a recession? The Phillips curve is central to the answers; its proper (nonlinear) specification reveals that the relationship is strong and frequency-dependent, and inflation is very persistent. We embed this empirically-successful Phillips curve – incorporating a supply-shocks variable – into a structural model. Identification is achieved using an underutilized data-dependent method. Despite imposing anchored inflation expectations and a rapid relaxation of supply-chain problems, we find that absent a recession, inflation will be >3% by the end of 2025. A simple welfare analysis supports a mild recession as preferred to an extended period of elevated inflation, under a typical loss function.