The observation that IMPUTE v2 can achieve lower error rates than IMPUTE v1 in Scenario A validates our new approach. At the same time, the absolute improvement is small, as can be seen in Figure 3 by comparing the separation between IMPUTE v1 and v2 with the separation between IMPUTE v1 and MACH, which typically yield very similar results in our experience. We have also performed separate experiments in which IMPUTE v2 achieves much higher phasing accuracy than IMPUTE v1 at SNPs in T, but where the improvements in HapMap-based imputation of SNPs in U remain modest (data not shown). We suggest that this disconnect between phasing accuracy and imputation accuracy is caused by the inherent limitations of a small reference panel; in other words, we posit that existing models would not attain substantially lower imputation error rates with the current HapMap panel even if we knew the phase of the study genotypes perfectly.