We also attempted to use a “coalescent-based” method for choosing custom reference panels (Pasaniuc et al. 2010), but we could not get it to produce accurate results on our data; see File S6 for details. We omitted another leading imputation method, MaCH (Li et al. 2010), because it was not computationally feasible with the full HapMap 3 panel at the time of these experiments. Both IMPUTE2 and MaCH have recently been made more efficient through “pre-phasing” of GWAS genotypes (the MaCH implementation is called “minimac”). While we did not evaluate these approaches here, we have found that pre-phasing is complementary to our khap approximation in preliminary experiments, as we explain in the Discussion. All else being equal, we would expect minimac to achieve similar accuracy to IMPUTE2 since both methods are based on the Li and Stephens (2003) model of DNA sequence variation, although further work may be needed to compare these methods in various contexts.