Environmental exposure data may improve statistical power in genetic studies when gene-environment interaction is present. However, resources invested in obtaining exposure data could instead be applied to measure disease status and genotype on more subjects. In a cohort-study setting, we consider the tradeoff between measuring only disease status and genotype for a larger study sample and measuring disease status, genotype, and environmental exposure for a smaller sample, under the gene-environment independence assumption in the study population. We focus on the power of tests for gene-disease association, applied in situations where a gene modifies risk of disease due to environmental exposure. Our results are equally applicable to exploratory genome-wide association studies and to more hypothesis-driven candidate gene investigations. We further consider the impact of misclassification for environmental exposures. We identify circumstances under which higher power is achieved via the larger study sample without measurements of environmental exposure.