The symmetry elements detected by the self-rotation and the Patterson functions, associated with strong correlations between the positions of the molecules in the asymmetric unit, are used to reduce the effective number of independent bodies to be located by the molecular replacement method. A distinction is made between `frustrated' crystallographic symmetries, i.e. those that are almost crystallographic ones, and `standard' non-crystallographic symmetries, which are taken into account by specific techniques. These have been successfully applied to many-body macromolecular crystal structures, with important savings in time and computational effort.