Our results provide some guidance as to how resources might best be targeted to identify genetic variation underlying the ‘missing’ heritability for complex traits that remains unexplained by recent GWAS. Although common CNVs seem highly unlikely to account for much of this missing heritability, the striking strength of purifying selection acting on exonic and intronic deletions suggests that CNVs might contribute appreciably to rare variants involved in common and rare diseases, and that study designs that focus on ascertaining rare sequence and structural variants will maximise power to detect new causal variation.