We present a new approach for estimation of the population-scaled mutation rate, , from microsatellite genotype data, using the recently introduced "product of approximate conditionals" framework. Comparisons with other methods on simulated data demonstrate that this new approach is attractive in terms of both accuracy and speed of computation. Our simulation experiments also demonstrate that, despite the theoretical advantages of full-likelihood-based methods, methods based on certain summary statistics (specifically, the sample homozygosity) can perform very competitively in practice.