Genome-wide association studies (GWASs) are an optimal design for discovery of disease risk loci for diseases whose underlying genetic architecture includes many common causal loci of small effect (a polygenic architecture). We consider two designs that deserve careful consideration if the true underlying genetic architecture of the trait is polygenic: parent-offspring trios and unscreened control subjects. We assess these designs in terms of quantification of the total contribution of genome-wide genetic markers to disease risk (SNP heritability) and power to detect an associated risk allele. First, we show that trio designs should be avoided when: (1) the disease has a lifetime risk > 1%; (2) trio probands are ascertained from families with more than one affected sibling under which scenario the SNP heritability can drop by more than 50% and power can drop as much as from 0.9 to 0.15 for a sample of 20,000 subjects; or (3) assortative mating occurs (spouse correlation of the underlying liability to the disorder), which decreases the SNP heritability but not the power to detect a single locus in the trio design. Some studies use unscreened rather than screened control subjects because these can be easier to collect; we show that the estimated SNP heritability should then be scaled by dividing by (1 - K × u)