At least 3 different types of computational model have been shown to account for various facets of both normal and impaired single word reading: (a) the connectionist triangle model, (b) the dual-route cascaded model, and (c) the connectionist dual process model. Major strengths and weaknesses of these models are identified. In the spirit of nested incremental modeling, a new connectionist dual process model (the CDP+ model) is presented. This model builds on the strengths of 2 of the previous models while eliminating their weaknesses. Contrary to the dual-route cascaded model, CDP+ is able to learn and produce graded consistency effects. Contrary to the triangle and the connectionist dual process models, CDP+ accounts for serial effects and has more accurate nonword reading performance. CDP+ also beats all previous models by an order of magnitude when predicting individual item-level variance on large databases. Thus, the authors show that building on existing theories by combining the best features of previous models--a nested modeling strategy that is commonly used in other areas of science but often neglected in psychology--results in better and more powerful computational models.