The main obstacle toab initiocrystal structure solution by powder data is the lack of accuracy in the single Bragg integrated intensity estimates. The two-stage method proves powerful for solving crystal structures from powder data: in the first stage, the integrated intensities and, consequently, the structure-factor moduli, are extracted from the pattern for each reflection; in the second stage, direct methods may be applied to estimate the phases of the structure factors. The greater the accuracy of the integrated intensities, the more efficient the phasing procedure. A new procedure is described, aiming at overcoming the tendency of the Le Bail algorithm [Le Bailet al.(1988).Mater. Res. Bull.23, 447–452] to equipartition the intensities of strongly overlapping reflections. It proves to be efficient for lowering the phase error in the phasing process. The procedure has been implemented in theEXPOprogram [Altomareet al.(1999).J. Appl. Cryst.32, 339–340].