Random forests are ensemble learning methods introduced by Breiman [Mach. Learn. 45 (2001) 5–32] that operate by averaging several decision trees built on a randomly selected subspace of the data set. Despite their widespread use in practice, the respective roles of the different mechanisms at work in Breiman’s forests are not yet fully understood, neither is the tuning of the corresponding parameters. In this paper, we study the influence of two parameters, namely the subsampling rate and the tree depth, on Breiman’s forests performance. More precisely, we prove that quantile forests (a specific type of random forests) based on subsampling and quantile forests whose tree construction is terminated early have similar performances, as long as their respective parameters (subsampling rate and tree depth) are well chosen. Moreover, experiments show that a proper tuning of these parameters leads in most cases to an improvement of Breiman’s original forests in terms of mean squared error.