The Single Variable Exchange algorithm is based on a simple idea; any model that can be simulated can be estimated by producing draws from the posterior distribution. We build on this simple idea by framing the Exchange algorithm as a mixture of Metropolis transition kernels and propose strategies that automatically select the more efficient transition kernels. In this manner we achieve significant improvements in convergence rate and autocorrelation of the Markov chain without relying on more than being able to simulate from the model. Our focus will be on statistical models in the Exponential Family and use two simple models from educational measurement to illustrate the contribution.