We find that variants discovered through large-scale sequencing have longer haplotypes than more common variants, and that imputation can perform well for both CNPs and low-frequency SNPs. Success was partial (as compared to common variants), and required a number of conditions: large reference panels, dense and accurate genotyping and good phasing. Moreover, some variants were not well imputed, although it is unclear if this is fundamental or due to a need for improved methods of imputation of lower frequency variants.