Uninterpretable electron-density maps were obtained using either MIRAS phases or MR phases in attempts to determine the structure of the type II restriction endonuclease SgrAI bound to DNA. While neither solution strategy was particularly promising (map correlation coefficients of 0.29 and 0.22 with the final model, respectively, for the MIRAS and MR phases and Phaser Z scores of 4.0 and 4.3 for the rotation and translation searches), phase combination followed by density modification gave a readily interpretable map. MR with a distantly related model located a dimer in the asymmetric unit and provided the correct transformation to use in averaging electron density between SgrAI subunits. MIRAS data sets with low substitution and MR solutions from only distantly related models should not be ignored, as poor-quality starting phases can be significantly improved. The bootstrapping strategy employed to improve the initial MIRAS phases is described.