Deploying machine learning (ML) models often requires both fairness and privacy guarantees. Both of these objectives present unique trade-offs with the utility (e.g., accuracy) of the model. However, the mutual interactions between fairness, privacy, and utility are less well-understood. As a result, often only one objective is optimized, while the others are tuned as hyper-parameters. Because they implicitly prioritize certain objectives, such designs bias the model in pernicious, undetectable ways. To address this, we adopt impartiality as a principle: design of ML pipelines should not favor one objective over another. We propose impartially-specified models, which provide us with accurate Pareto frontiers that show the inherent trade-offs between the objectives. Extending two canonical ML frameworks for privacy-preserving learning, we provide two methods (FairDP-SGD and FairPATE) to train impartially-specified models and recover the Pareto frontier. Through theoretical privacy analysis and a comprehensive empirical study, we provide an answer to the question of where fairness mitigation should be integrated within a privacy-aware ML pipeline.