Key message <p><b>Improving a hybrid by transferring partially dominant alleles from one parent to the other is feasible if the median level of dominance is moderate and prediction accuracy is high.</b></p> Abstract <p>Convergent improvement within a <i>P</i>₁ × <i>P</i>₂ single-cross hybrid&#xa0;attempts to transfer partially dominant favorable alleles from <i>P</i>₁ to <i>P</i>₂ and from <i>P</i>₂ to <i>P</i>₁. My objective in this simulation study was to determine if convergent improvement is a feasible procedure to develop a better single cross. Heterozygote effects (<i>d</i>) and homozygote effects (<i>a</i>) at quantitative trait loci (QTL) were resampled from an empirical distribution of genomewide marker estimates of <i>d</i> and <i>a</i> for maize (<i>Zea mays</i> L.) grain yield. The <i>d</i> values were scaled (<i>d</i> scale = 30%, 45%, and 60%) to account for the known upward bias when <i>d</i>/<i>a</i> ratios at markers are used to estimate <i>d</i>/<i>a</i> ratios at QTL. Convergent improvement led to positive responses to selection when only 30 QTL controlled the trait. When 250 QTL controlled the trait, convergent improvement led to a positive response when the <i>d</i> scale was 30% but not when the <i>d</i> scale was 60%. For the intermediate <i>d</i> scale of 45%, responses were positive in later backcross generations and when prediction accuracy was 0.60 or 0.80. The largest response was achieved with only one cycle of genomewide recurrent selection; additional cycles compromised the gains achieved from the final step of phenotypic selection among single crosses. Overall, the results suggested that success in convergent improvement is a possibility but not a certainty in maize, and that more consistent results would be expected in species such as rice (<i>Oryza sativa</i> L.) that show weaker heterosis than maize.</p>