In this study, a simulation-based method for computing joint maximum likelihood estimates of cognitive diagnosis model parameters is proposed. The central theme of the approach is to reduce the complexity of models to focus on their most critical elements. In particular, an approach analogous to joint maximum likelihood estimation is taken, and the latent attribute vectors are regarded as structural parameters, not parameters to be removed by integration with this approach, the joint distribution of the latent attributes does not have to be specified, which reduces the number of parameters in the model. The Markov Chain Monte Carlo algorithm is used to simultaneously evaluate and optimize the likelihood function. This streamlined approach performed as well as more traditional methods for models such as the DINA, and affords the opportunity to fit more complicated models in which other methods may not be feasible.