Measurement error and biological variability generate distortions in quantitative phenotypic data. In longitudinal studies with repeated measurements, the multiple measurements provide a route to reduce noise and correspondingly increase the strength of signals in genome-wide association studies (GWAS).To optimize noise correction, we have developed Shrunken Average (SHAVE), an approach using a Bayesian Shrinkage estimator. This estimator uses regression toward the mean for every individual as a function of (1) their average across visits; (2) their number of visits; and (3) the correlation between visits. Computer simulations support an increase in power, with results very similar to those expected by the assumptions of the model. The method was applied to a real data set for 14 anthropomorphic traits in ∼6000 individuals enrolled in the SardiNIA project, with up to three visits (measurements) for each participant. Results show that additional measurements have a large impact on the strength of GWAS signals, especially when participants have different number of visits, with SHAVE showing a clear increase in power relative to single visits. In addition, we have derived a relation to assess the improvement in power as a function of number of visits and correlation between visits. It can also be applied in the optimization of experimental designs or usage of measuring devices. SHAVE is fast and easy to run, written in R and freely available online.