Automated predictions require explanations to be interpretable by humans. Past work used attention and rationale mechanisms to find words that predict the target variable of a document. Often though, they result in a tradeoff between noisy explanations or a drop in accuracy. Furthermore, rationale methods cannot capture the multi-faceted nature of justifications for multiple targets, because of the non-probabilistic nature of the mask. In this paper, we propose the Multi-Target Masker (MTM) to address these shortcomings. The novelty lies in the soft multi-dimensional mask that models a relevance probability distribution over the set of target variables to handle ambiguities. Additionally, two regularizers guide MTM to induce long, meaningful explanations. We evaluate MTM on two datasets and show, using standard metrics and human annotations, that the resulting masks are more accurate and coherent than those generated by the state-of-the-art methods. Moreover, MTM is the first to also achieve the highest F1 scores for all the target variables simultaneously.