This paper investigates core inflation defined as the best predictor of inflation. I compare forecasts obtained using the mean, weighted median, trimmed mean, and less food and energy inflation rates for the consumer price index and the personal consumption expenditure deflator for the current U.S. monetary policy regime. Another issue addressed is that of the systematic bias that exists due to the differences in means of these measures. I test whether correcting for this bias can lead to better inflation forecasts. This paper finds that adjusting for bias improves forecasting and that the weighted median is a better forecaster than the alternative measures and thus is a good measure of core inflation.