While deep neural networks are highly effective at solving complex tasks, large pre-trained models are commonly employed even to solve consistently simpler downstream tasks, which do not necessarily require a large model's complexity. Motivated by the awareness of the ever-growing AI environmental impact, we propose an efficiency strategy that leverages prior knowledge transferred by large models. Simple but effective, we propose a method relying on an Entropy-bASed Importance mEtRic (EASIER) to reduce the depth of over-parametrized deep neural networks, which alleviates their computational burden. We assess the effectiveness of our method on traditional image classification setups. The source code will be publicly released upon acceptance of the article.