We develop a class of demand models for differentiated products. The new mod- els facilitate the BLP method (Berry et al., 1995) while numerical inversion of the demand system is not required. They can accommodate rich patterns of substitution and complementarity while being easily estimated with standard regression techniques and allowing very large choice sets. We use the new models to describe markets for differentiated products that exhibit segmentation according to several dimensions and illustrate their application by estimating demand for cereals in Chicago.