In order to improve the storage capacity of the Hopfield model, we develop a version of the dreaming algorithm, called daydreaming, that is not destructive and that converges asymptotically to a stationary coupling matrix. When trained on random uncorrelated examples, the model shows optimal performance in terms of the size of the basins of attraction of stored examples and the quality of reconstruction. We also train the daydreaming algorithm on correlated data obtained via the random-features model and argue that it exploits the correlations to increase even further the storage capacity and the size of the basins of attraction.