The traditional CPI measure has many drawbacks, when used for very different purposes, and it is not at all surprising that a great deal of work has been devoted to its improvement. Besides seasonal adjustment, various other techniques have been developed to find the “core” inflation index. Although a generally accepted definition of core inflation does not exist, the literature converges towards identifying certain desirable properties that a “good” core index must possess. After reviewing the literature we describe how the publication of a core index fits into the monetary policy strategy of the National Bank of Hungary. Monetary policy both in the form of setting the instruments and by communicating to the public is geared to arrive at a mutual understanding with the markets. By publishing a core inflation index, the NBH aims at providing the public with a price measure that can function as a co-ordination device between policy makers and market participants. As the “index number” problem is clearly connected with relative price changes, we analyze in some depth this issue, too. We argue that there have been clearly visible tendencies in relative price developments that jeopardize some of the traditional uses of inflation measures. Our results suggest that a substantial amount of noise and apparent seasonality have come about as a result of government decisions. Finally we muster some possible procedures to define core indices in Hungary, by comparing their smoothness and forecasting ability from several points of view. Our conclusion is that there is no overwhelming reason to abandon the current “exclusion” approach toward the core.