Experiences with the molecular-replacement program Beast have shown that maximum-likelihood rotation targets are more sensitive to the correct orientation than traditional targets. However, this comes at a high computational cost: brute-force rotation searches can take hours or even days of computation time on current desktop computers. Series approximations to the full likelihood target have been developed that can be computed by fast Fourier transforms in minutes. These likelihood-enhanced targets are more sensitive to the correct orientation than the Crowther fast rotation function and they take advantage of information from partial solutions. The likelihood-enhanced rotation targets have been implemented in the program Phaser.