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An algorithm for Method 3 for estimation of components of variance in a mixed model including fixed herd-year-season, genetic groups, and random sires nested within groups is presented. Computational aspects of the algorithm are discussed and compared with those of a new method of Henderson's. The new method involves equating quadratic forms based on approximate best linear unbiased prediction solutions to their expected values. Relative computing effort for the two methods depended on the ease of eliminating equations for fixed effects and on the number of traits. Numerical estimates from the two methods were similar. When the Method 3 estimate of the sire component of variance was not close to zero, the new method rapidly converged during iteration even when the a priori variance component ratio was not close to the final estimate.