Molecular dynamics simulations require barostats to be performed at a constant pressure. The usual recipe is to employ the Berendsen barostat first, which displays a first-order volume relaxation efficient in equilibration but results in incorrect volume fluctuations, followed by a second-order or a Monte Carlo barostat for production runs. In this paper, we introduce stochastic cell rescaling, a first-order barostat that samples the correct volume fluctuations by including a suitable noise term. The algorithm is shown to report volume fluctuations compatible with the isobaric ensemble and its anisotropic variant is tested on a membrane simulation. Stochastic cell rescaling can be straightforwardly implemented in the existing codes and can be used effectively in both equilibration and production phases.