We introduce novel algorithms for generating random solutions from a uniform distribution over the solutions of a boolean satisfiability problem. Our algorithms operate in two phases. In the first phase, we use a recently introduced SampleSearch scheme to generate biased samples while in the second phase we correct the bias by using either Sampling/Importance Resampling or the Metropolis- Hastings method. Unlike state-of-the-art algorithms, our algorithms guarantee convergence in the limit. Our empirical results demonstrate the superior performance of our new algorithms over several competing schemes.