When a character has a large additive genetic component in its variance, general combining ability estimates may be used for predicting cross performance. Further, if emphasis is placed on the ranks of the general combining abilities in a diallel rather than on their numerical values, the incomplete partial diallel is a powerful tool for parental selection. In a self pollinating species, if general combining ability effects are equal to or greater than specific combining ability effects, 20% of the partial diallel is found to give enough information for accurate ranking of the parental general combining abilities. A generalised method for calculating general combining abilities from incomplete partial diallels is presented and tested by computer simulation over a large range of genetic population parameters.