The practicability of a specific procedure for within-herd genetic evaluation of beef cattle for weaning weight was tested with a data set of 503 Angus weaning weight records obtained from 1958 through 1976. Three different sets of genetic evaluations were obtained with the same model. The model included herd-year means, direct additive genetic values, maternal additive genetic values and random environmental errors. The evaluations of set 1 were best linear unbiased predictions (BLUP) with a full complement of equations, i.e., one for both the direct and maternal trait of all animals in the pedigree. To reduce computational load by eliminating predictions of little interest, either the direct or maternal equation for certain animals was deleted from the full complement. The resulting set 2 evaluations were also BLUP. A third method permitted further reduction in the number of equations and, therefore, computations, but the resulting set 3 evaluations were not BLUP. Thirty-seven and 43% less computer time was necessary to obtain evaluations of sets 2 and 3, respectively, than to obtain the set 1 evaluations. The correlations among the three sets of evaluations were very high, the average differences in rank small and the maximum absolute differences of predictions of the same genetic value small. The genetic, environmental and phenotypic trends obtained from each set of evaluations were similar. The results indicated that the genetic progress made from selection decisions based on evaluation sets 1, 2 and 3 would be similar.