The official U.S. Consumer Price Index (CPI) is a Laspeyres index. An alternative form of the index known as the geometric mean (GeoMeans) index is scheduled to be published in 1997. In this paper, rental housing data have been studied with regard to rent levels, to the average weights attributed to these levels and to the average rate of rental price change at these levels. These weights are quantity-based. A two-partition model is constructed, with "low" rents compared with "higher" rents. Simulations are run comparing Laspeyres and GeoMeans index results. The differences between the two indexes are plotted against the rate of price change in the "low" rent sector. In the simulations, all the other factors are treated as fixed. A smooth (quadratic) curve results, and the GeoMeans indexes are shown to score consistently higher than the Laspeyres indexes.