Heritability estimates of bolting percentage (BP), pink root (PR) and Fusarium basal rot (FBR) incidences, and percentage of single centered (PSC) bulbs were calculated for an intermediate-day, open-pollinated onion population using selection response and half-sib (HS) family analyses. BP was determined by counting the number of seedstalks per plot when the population was seeded at an earlier planting date to induce bolting. PR and FBR incidences were determined by rating 30 bulbs/plot for the severity of PR and FBR, and calculated an incidence rate from the number of infected bulbs out of 30 rated. The PSC bulbs was determined by cutting transversely 30 bulbs at the vertical center of the bulb and looking for the presence of a single growing point or multiple growing points within 1.3 cm from the center of the bulb. Families were also evaluated for bulb quality that consisted of shape, size, maturity, firmness, number of scale layers, and dry outer scale thickness, adherence, retention, and color. Families were selected based upon an index that equally weighted BP, PR and FBR incidences, PSC bulbs, and bulb quality. No progress was made for BP even though the narrow sense heritability (h2) estimate was 0.51. PR and FBR incidence was reduced by 18% and 12%, respectively, and realized heritability (RH) estimates of 0.65 and 0.60, respectively, were calculated. h2 estimates calculated through HS family analysis was 0.46 and 0.37, respectively, for these two traits. Very little progress was made for the PSC bulbs and this was reflected in a RH estimate of 0.17. However, the h2 estimate was 0.71, suggesting that progress should be possible.