We investigate the role of assortative mating in speciation using the sympatric model of Derrida and Higgs. The model explores the idea that genetic differences create incompatibilities between individuals, preventing mating if the number of such differences is too large. Speciation, however, only happens in this mating system if the number of genes is large. Here we show that speciation with small genome sizes can occur if assortative mating is introduced. In our model individuals are represented by three chromosomes: one responsible for reproductive compatibility, one for coding the trait on which assortativity will operate, and a neutral chromosome. Reproduction is possible if individuals are genetically similar with respect to the first chromosome, but among these compatible mating partners, the one with the most similar trait coded by the second chromosome is selected. We show that this type of assortativity facilitates speciation, which can happen with a small number of genes in the first chromosome. Species, classified according to reproductive isolation, dictated by the first chromosome, can display different traits values, as measured by the second and the third chromosomes. Therefore, species can also be identified based on similarity of the neutral trait, which works as a proxy for reproductive isolation.