Understanding the decisions made by deep neural networks is essential in high-stakes domains such as medical imaging and autonomous driving. Yet, these models often lack transparency, particularly in computer vision. Prototypical-parts-based neural networks have emerged as a promising solution by offering concept-level explanations. However, most are limited to fine-grained classification tasks, with few exceptions such as InfoDisent. InfoDisent extends prototypical models to large-scale datasets like ImageNet, but produces complex explanations. We introduce Sparse Information Disentanglement for Explainability (SIDE), a novel method that improves the interpretability of prototypical parts through a dedicated training and pruning scheme that enforces sparsity. Combined with sigmoid activations in place of softmax, this approach allows SIDE to associate each class with only a small set of relevant prototypes. Extensive experiments show that SIDE matches the accuracy of existing methods while reducing explanation size by over $90\%$, substantially enhancing the understandability of prototype-based explanations.