Discrete models are important to reduce the complexity of the protein folding problem. However, a compromise must be made between the model complexity and the accuracy of the model. Previous work by Park and Levitt has shown that the protein backbone can be modeled with good accuracy by four state discrete models. Nonetheless, for abinitio protein folding, the side chains are important to determine if the structure is physically possible and well packed. We extend the work of Park and Levitt by taking into account the positioning of the side chain in the evaluation of the accuracy. We show that the problem becomes much harder and more dependent on the type of protein being modeled. In fact, the structure fitting method used in their work is no longer adequate to this extended version of the problem. We propose a new method to test the model accuracy. The presented results show that, for some proteins, the discrete models with side chains cannot achieve the accuracy of the backbone discrete models. Nevertheless, for the majority of the proteins an RMSD of four angstrom or less is obtained, and, for many of those, we reach an accuracy near the two angstrom limit. These results prove that discrete models can be used in protein folding for obtaining low resolution models. Since the side chains are already present in the models, the refinement of these solutions is simpler and more effective.