Broad sense heritabilities were estimated in three long-term cocoa clone trials in Ghana, with 20, 18 and 15 entries. They were 0.15, 0.05 and 0.15 for yield in pods per plant, and 0.26, 0.19 and 0.40 for incidence of ‘bad’ pods, mostly due to black pod disease, caused by infection with Phytophthora spp. The low heritability of single plant yield, which has been known for 80 years, has been widely overlooked in cocoa research and extension, compromising the success of clone selection programmes. The heritability of the incidence of black pod disease is high enough to justify mass selection where family level data are not available. The findings will be applied in a new large-scale programme in Ghana to select clones that are high yielding in the presence of P. megakarya.