This work addresses the situation where a black-box model with good predictive performance is chosen over its interpretable competitors, and we show interpretability is still achievable in this case. Our solution is to find an interpretable substitute on a subset of data where the black-box model is \emph{overkill} or nearly overkill while leaving the rest to the black-box. This transparency is obtained at minimal cost or no cost of the predictive performance. Under this framework, we develop a Hybrid Rule Sets (HyRS) model that uses decision rules to capture the subspace of data where the rules are as accurate or almost as accurate as the black-box provided. To train a HyRS, we devise an efficient search algorithm that iteratively finds the optimal model and exploits theoretically grounded strategies to reduce computation. Our framework is \emph{agnostic} to the black-box during training. Experiments on structured and text data show that HyRS obtains an effective trade-off between transparency and interpretability.