Recent experiments at free-electron laser X-ray sources have been able to resolve the intensity distributions about Bragg peaks in nanocrystals of large biomolecules. Information derived from small shifts in the peak positions augment the Bragg samples of the particle intensity with samples of its gradients. Working on the assumption that the nanocrystal is entirely generated by lattice translations of a particle, an algorithm is developed that reconstructs the particle from intensities and intensity gradients. Unlike traditional direct phasing methods that require very high resolution data in order to exploit sparsity of the electron density, this method imposes no constraints on the contrast other than positivity and works well at low resolution. Successful reconstructions are demonstrated with simulated P1 lysozyme nanocrystal data down to a signal-to-noise ratio of 2 in the intensity gradients. © 2013 International Union of Crystallography Printed in Singapore - all rights reserved.