Stochastic simulation was used to study the effect of using full data and pedigree structure vs more recent data and pedigree structure to obtain best linear unbiased predictors (BLUP) of breeding values for single trait selection. Simulations used heritabilities of 0.10 and 0.50, with a population structure of 20 sires each mated to two dams, each producing 10 progeny, with 11 hatches from an unselected base population under both discrete and overlapping generations. Selection of parents was based on BLUP of breeding values using an animal model. The use of the last two generations of data and pedigrees gave the same selection response as when using full data and pedigree structure, for both heritabilities. Under discrete generations with use of only the last generation data and pedigree, which is similar to phenotypic evaluation, response to selection decreased by 21 and 3.8% at Generation 10 compared to selection response when using the full data and pedigree for heritabilities of 0.10 and 0.50, respectively. Corresponding decreases in inbreeding were 72 and 37%. The amount of central processing unit time for genetic evaluation when using the last six, four, and two generations of data and pedigree was reduced to 70, 40, and 11% of that when using the full data set, for a heritability of 0.10 and discrete generations. Very similar values were observed for a heritability of 0.50 and also under overlapping generations.