Genetic effects for common variants affecting complex disease risk are subtle. Single genome-wide association (GWA) studies are typically underpowered to detect these effects, and combination of several GWA data sets is needed to enhance discovery. The authors investigated the properties of the discovery process in simulated cumulative meta-analyses of GWA study-derived signals allowing for potential genetic model misspecification and between-study heterogeneity. Variants with null effects on average (but also between-data set heterogeneity) could yield false-positive associations with seemingly homogeneous effects. Random effects had higher than appropriate false-positive rates when there were few data sets. The log-additive model had the lowest false-positive rate. Under heterogeneity, random-effects meta-analyses of 2-10 data sets averaging 1,000 cases/1,000 controls each did not increase power, or the meta-analysis was even less powerful than a single study (power desert). Upward bias in effect estimates and underestimation of between-study heterogeneity were common. Fixed-effects calculations avoided power deserts and maximized discovery of association signals at the expense of much higher false-positive rates. Therefore, random- and fixed-effects models are preferable for different purposes (fixed effects for initial screenings, random effects for generalizability applications). These results may have broader implications for the design and interpretation of large-scale multiteam collaborative studies discovering common gene variants.