This article has three basic themes. First, the structure of the St. Louis Model (used for years at the St. Louis Fed to provide alternate scenarios for the response of inflation, output, and the unemployment rate under different monetary policy assumptions) can be simplified and its predictive performance improved. Second, the St. Louis Model’s specification of the demand slack variable in its Phillips curve may bias the equation’s estimate of inflation’s response to demand slack and, therefore, could yield an overly optimistic assessment of the cost of reducing inflation in terms of the higher unemployment during the transition to a lower rate of inflation. Third, a monetarist reduced-form equation for inflation, in which inflation depends directly on current and past monetary growth, is not inconsistent with the existence of a Phillips curve. This is demonstrated by comparing the predictive performance and policy implications of two variations of the St. Louis Model—one incorporating a Phillips curve, the other a monetarist reduced-form for inflation. Both versions outperform the St. Louis Model’s inflation predictions, and both yield nearly identical predictions and policy multipliers.