Although discrete hours choice models have become the workhorse in labor supply analyses. Yet, they are often criticized for being a black box due to their numerous underlying modeling assumptions, with respect to, e.g., the functional form, unobserved error components or several exogeneity assumptions. In this paper, we open the black box and show how these assumptions affect the statistical fit of the models and, more importantly, the estimated outcomes, i.e., estimated labor supply elasticities. In total we estimate 2,219 different model specifications. Our results show that the specification of the utility function is not crucial for performance and predictions of the model. We find however that the estimates are extremely sensitive to the treatment of the wages a neglected dimension so far. We show that, e.g., the choice between predicting wages for the full sample instead of using predicted wages only for non-workers two methods frequently used increases labor supply elasticities by up to 100 percent. As a consequence, we propose a new estimation strategy which overcomes the highly restrictive but commonly made assumption of independence between wages and the labor supply decision.