Abstract We here describe the maximum likelihood gyre method implemented in Phaser for optimizing the orientation and relative position of rigid body fragments of a model after the orientation of the model has been identified, but before the model has been positioned in the unit cell, and also the related gimble method, for refinement of rigid body fragments of the model after positioning. Gyre-refinement helps to lower the root-mean-square atomic displacements between model and target molecular replacement solutions for the test case antibody Fab(26-10), and improves structure solution with Arcimboldo-Shredder.