Publication of indexes measuring changes in prices of retail, wholesale, export, and import items is an important part of many governmental statistics programs. One form of price index that is often used is the fixed-base Laspeyres, in which a fixed market basket of goods is priced over time. This article introduces a new class of multiplicative estimators of Laspeyres indexes. The optimum within the class is derived for long-term price change and compared with two other members of the class when used for estimating both long-term and short-term change. Theoretical properties are derived under a model in which long-term relative price changes for individual items have common within-stratum means and are correlated over time. Theory for long-term and short-term change estimators is tested in a simulation study in which a large number of stratified probability samples is selected from a population extracted from items priced for the U.S. consumer price index.