The primary challenge for practitioners with multiple \textit{post-hoc gradient-based} interpretability methods is to benchmark them and select the best. Using information theory, we represent finding the optimal explainer as a rate-distortion optimization problem. Therefore : \begin{itemize} \item We propose an information-theoretic test \verb|InfoExplain| to resolve the benchmarking ambiguity in a model agnostic manner without additional user data (apart from the input features, model, and explanations). \item We show that \verb|InfoExplain| is extendable to utilise human interpretable concepts, deliver performance guarantees, and filter out erroneous explanations.\end{itemize}The adjoining experiments, code and data will be released soon.