Contextual Importance and Utility (CIU) is a model-agnostic method for producing situation- or instance-specific explanations of the outcome of so-called black-box systems. A major difference between CIU and other outcome explanation methods (also called post-hoc methods) is that CIU produces explanations without producing any intermediate interpretable model. CIU’s notion of importance is similar as in Decision Theory but differs from how importance is defined for other outcome explanation methods. Utility is also a well-known concept from Decision Theory that is largely ignored in current Explainable AI research. CIU is here validated by providing explanations for the two popular medical data sets - heart disease and breast cancer in order to show the applicability of CIU explanations on medical predictions and with different black-box models. The explanations are compared with corresponding ones produced by the Local Interpretable Model-agnostic Explanations (LIME) method [17], which is currently one of the most used post-hoc explanation methods. The paper’s main contribution is to provide new CIU results and insights on several benchmark data sets and showing in what way CIU differs from LIME-based explanations.