Current methods for Black-Box NLP interpretability, like LIME or SHAP, are based on altering the text to interpret by removing words and modeling the Black-Box response. In this paper, we outline limitations of this approach when using complex BERT-based classifiers: The word-based sampling produces texts that are out-of-distribution for the classifier and further gives rise to a high-dimensional search space, which can't be sufficiently explored when time or computation power is limited. Both of these challenges can be addressed by using segments as elementary building blocks for NLP interpretability. As illustration, we show that the simple choice of sentences greatly improves on both of these challenges. As a consequence, the resulting explainer attains much better fidelity on a benchmark classification task.