Optimized docking of models into cryo-EM maps requires exploiting an understanding of the signal expected in the data to minimize the calculation time while maintaining sufficient signal. The likelihood-based rotation function used in crystallography can be employed to establish plausible orientations in a docking search. A phased likelihood translation function yields scores for the placement and rigid-body refinement of oriented models. Optimised strategies for choices of the resolution of data from the cryo-EM maps to use in the calculations and the size of search volumes are based on expected log-likelihood-gain scores, computed in advance of the search calculation. Tests demonstrate that the new procedure is fast, robust and effective at placing models into even challenging cryo-EM maps.