Narrow-sense heritability estimates were computed for five fruit quality characteristics and their weighted total index. Grit content and skin russeting were moderately heritable traits, while flesh texture, flavor, appearance, and the weighted total score were of relatively low heritability. Within sub-populations of crosses, defined by the species ancestry of the parents, the relative magnitudes of heritabilities for each trait varied, but were in general agreement with those for the entire population. The general combining ability variances were 4.5 to 12.0 times those for specific combining ability, although both were statistically significant for all traits and the weighted quality index. The species ancestry of a parent had no effect on its general combining ability rank. While selection of individual seedlings on the basis of their own phenotype will result in genetic improvement for grit and russet, selection based on a combination of full-sib family means and individual phenotypes is recommended for flavor, texture, appearance, and overall fruit quality.