Decision-making processes have increasingly come to rely on sophisticated machine learning tools, raising concerns about the fairness of their predictions with respect to any sensitive groups. The widespread use of commercial black-box machine learning models necessitates careful consideration of their legal and ethical implications on consumers. In situations where users have access to these "black-box" models, a key question emerges: how can we mitigate or eliminate the influence of sensitive attributes, such as race or gender? We propose towerDebias (tDB), a novel approach designed to reduce the influence of sensitive variables in predictions made by black-box models. Using the Tower Property from probability theory, tDB aims to improve prediction fairness during the post-processing stage in a manner amenable to the Fairness-Utility Tradeoff. This method is highly flexible, requiring no prior knowledge of the original model's internal structure, and can be extended to a range of different applications. We provide a formal improvement theorem for tDB and demonstrate its effectiveness in both regression and classification tasks, underscoring its impact on the fairness-utility tradeoff.