Vision transformers (ViT) have been of broad interest in recent theoretical and empirical works. They are state-of-the-art thanks to their attention-based approach, which boosts the identification of key features and patterns within images thanks to the capability of avoiding inductive bias, resulting in highly accurate image analysis. Meanwhile, neoteric studies have reported a “sparse double descent” phenomenon that can occur in modern deep-learning models, where extremely over-parametrized models can generalize well. This raises practical questions about the optimal size of the model and the quest over finding the best trade-off between sparsity and performance is launched: are Vision Transformers also prone to sparse double descent? Can we find a way to avoid such a phenomenon? Our work tackles the occurrence of sparse double descent on ViTs. Despite some works that have shown that traditional architectures, like Resnet, are condemned to the sparse double descent phenomenon, for ViTs we observe that an optimally-tuned ℓ2 regularization relieves such a phenomenon. However, everything comes at a cost: optimal lambda will sacrifice the potential compression of the ViT.