Computational methods to explore posterior distributions, in particular Markov chain Monte Carlo (MCMC), have played a dominant role in Bayesian statistics over the last 30 years. These methods have enabled statisticians and researchers to tackle problems that defy closed-form solution, greatly expanding the scope of Bayesian analysis. Joseph's ingenious DoIt algorithm uses ideas developed over the last 20-25 years on statistical modeling of deterministic functions to develop a direct approximation to complex posterior distributions, without the need for the large sequential samples required by MCMC. The method can be applied to a wide variety of problems and offers the promise of accurate results with substantially reduced computing. The approximation is a weighted sum of Gaussians, which leads to the significant advantages that it is simple to normalize and it is easier to compute marginal densities. We think that the method has great potential and applaud Dr. Joseph for this important new idea. Our comments focus on some issues where we think further work might lead to additional improvements in the method.