What, if anything, does the low (<5%) proportion of trait-associated SNPs that might plausibly be tagging a causal CNV tell us about the contribution of common (MAF >5%) CNVs to complex disease susceptibility? The fact that most (77%) of our common genotyped CNVs are well-tagged by SNPs suggests that existing GWAS studies have already indirectly screened for the potential effect of these variants relatively effectively. By modelling the ascertainment of genotyped CNVs in this study (Supplementary Methods), we estimate that we have genotyped ~25–35% of all common CNVs greater than 1 kb in size. Thus, unless ungenotyped and poorly tagged common CNVs have a much higher effect on disease risk than the well-tagged common CNVs we were able to genotype, extrapolating from our incomplete ascertainment of CNV could only explain a small minority of the disease risk already accounted for existing GWAS studies, let alone the larger (for most diseases) bulk of ‘missing’ heritability that remains unaccounted for by GWASs. Further large-scale association studies that directly assay all classes of CNV are required to precisely estimate the contribution of common CNVs to the heritability of complex traits.