This paper examines the recent behavior of core inflation in the United States. We specify a simple Phillips curve based on the assumptions that inflation expectations are fully anchored at the Federal Reserve's target, and that labor-market slack is captured by the level of shortterm unemployment. This equation explains inflation behavior since 2000, including the failure of high total unemployment since 2008 to reduce inflation greatly. The fit of our equation is especially good when we measure core inflation with the Cleveland Fed's series on weighted median inflation. We also propose a more general Phillips curve in which core inflation depends on short-term unemployment and on expected inflation as measured by the Survey of Professional Forecasters. This specification fits U.S. inflation since 1985, including both the anchored-expectations period of the 2000s and the preceding period when expectations were determined by past levels of inflation.