increasing longterm response by selecting for favorable minor alleles longterm response of genomic selection can be improved by considering allele frequencies of selected markers or quantitative trait loci qtls a previous formula to weight allele frequency of favorable minor alleles was tested and 2 new formulas were developed the previous formula used nonlinear weights based on square root of frequency of the favorable allele the new formulas included a parameter to balance long and shortterm progress one used square root and the other used simple linear weights the formulas were tested by simulation of 20 generations population size of 3000 for each generation with direct selection on 3000 qtls 100 per chromosome a qtl distribution with normally distributed allele effects and a heavytailed distribution were tested optimum from simulation was applied to data from holstein jersey and brown swiss dairy cattle to compare differences of adjusted and official genomic evaluations from simulation optimum was 04 for the heavytailed qtl distribution but only 01 or 02 for a normal distribution the previous formula had slower response than unweighted selection in early generations and did not recover by generation 20 longterm response was slightly greater with the new formulas than with unweighted selection the linear formula may be best for routine use because of more progress in early generations compared to nonlinear formula official and adjusted us evaluations based on actual genotypes and estimated marker effects were correlated by 0994 for holsteins and jerseys and 0989 for brown swiss using linear weighting of allele frequency which was higher than nonlinear weighting the difference between adjusted and official evaluations was highly correlated negatively with an animals average genomic relationship to the population thus strategies to reduce genomic inbreeding may achieve almost as much longterm progress as selection of favorable minor alleles