We reconsider the identification and estimation of Gorman-Lancaster-style hedonic models of demand for differentiated products in the spirit of Sherwin Rosen. We generalize Rosen's first stage to account for product characteristics that are not observed and to allow the hedonic pricing function to have a general nonseparable form. We take an alternative semiparametric approach to Rosen's second stage in which we assume that the parametric form of utility is known, but we place no restrictions on the aggregate distribution of utility parameters. If there are only a small number of products, we show how to construct bounds on individuals' utility parameters, as well as other economic objects such as aggregate demand and consumer surplus. We apply our methods to estimating the demand for personal computers.