Genomewide markers may help untangle unfavorable trait correlations that hinder cultivar development. Our objectives were to determine (i) if genomewide markers can be used to partition trait effects into independent and correlated portions, and (ii) if selection on the independent portion leads to larger responses than selection on the entire trait. We compared a standard genomewide selection model (control model) with a genomewide selection model that targeted the independent portion of a trait (independent model). We conducted four cycles of genomewide selection in two biparental maize (Zea mays L.) populations. In Population 1, Cycle 4 responses to selection with the independent model (vs. the control model, in parentheses) were 1.03 Mg ha−1 (vs. 1.40 Mg ha−1) for grain yield, 0.38 g kg−1 (vs. −7.98 g kg−1) for moisture, and 6.50 cm (vs. 18.75 cm) for plant height. In Population 2, responses were 0.19 Mg ha−1 (vs. −0.27 Mg ha−1) for grain yield, 3.83 g kg−1 (vs. 6.60 g kg−1) for moisture, and 4.30 cm (vs. 7.80 cm) for plant height. None of the responses were significantly different (P = 0.05) between the independent model and the control model at each cycle of genomewide selection. These nonsignificant differences were explained by the low proportions (R2 < 14%) of the trait variation accounted for by the independent portion of the trait. We conclude that separating quantitative traits into correlated and independent portions is infeasible.