Advances in Implicit Neural Representations (INR) have motivated research on domain-agnostic compression techniques. These methods train a neural network to approximate an object, and then store the weights of the trained model. For example, given an image, a network is trained to learn the mapping from pixel locations to RGB values. In this paper, we propose L$_0$onie, a sparsity-constrained extension of the COIN compression method. Sparsity allows to leverage the faster learning of overparameterized networks, while retaining the desirable compression rate of smaller models. Moreover, our constrained formulation ensures that the final model respects a pre-determined compression rate, dispensing of the need for expensive architecture search.