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There is considerable interest in bovine DNA-level polymorphic marker loci as a means of mapping quantitative trait loci (QTL) of economic importance in cattle. Progeny of a sire heterozygous for both a marker locus and a linked QTL, which inherit different alleles for the marker, will have different trait means. Based on this, power to detect QTL, as a function of QTL effect, heritability of the trait, and number of animals tested was determined for 1) daughter design, marker genotype and quantitative trait values assessed on daughters of sires heterozygous for the markers; and 2) granddaughter design, a newly devised alternative design in which marker genotype is determined on sons of heterozygous sires and quantitative trait value measured on daughters of the sons. For equal numbers of assays, power increased with the number of daughters per sire (design 1) and sons per grandsire (design 2). For equal power and heritability less than or equal to .2, design 2 required half as many marker assays as design 1, e.g., with heritability of .2, QTL effect of .2 SD units, and type 1 error of .01, power was .70 if 400 daughters of each of 10 sires were assayed for the markers and .95 if markers were assayed on 100 sons of each of 20 sires with 50 granddaughters per son.