There is still considerable dispute about the magnitude of labor supply elasticities. While differences in micro and macro estimates are recently attributed to frictions and adjustment costs, we show that relatively low labor supply elasticities derived from microeconometric models can also be explained by modeling assumptions with respect to wages. Specifically, we estimate 3,456 structural labor supply models each representing a plausible combination of frequently made choices. While most model assumptions do not systematically affect labor supply elasticities, our analysis shows that the results are very sensitive to the treatment of wages. In particular, the often-made but highly restrictive independence assumption between preferences and wages is key. To overcome this restriction, we propose a flexible estimation strategy that nests commonly used models. We show that loosening the exogeneity assumption leads to labor supply elasticities that are much higher.