Many species of birds have a characteristic clutch size which is either fixed at k or is of the form k or k + 1 for some appropriate integer k. For example, the ground-living pigeons lay two eggs, the white stork four and the sulphur-crested cockatoo two and rarely three. The spotted nightjar lays one egg and the white-tailed nightjar lays two. The (European) swift lays two or three eggs, the (Australian) wood swallows lay three or four eggs and a number of (Australian) finches lay five or six eggs. These clutch sizes should be the result of evolutionary forces and it could be expected that the clutch size, for a particular species and environment, is the one which results in maximization of the probability of survival of the species to each time point t. It is consequently of interest to see whether it is possible to prescribe a population process which provides a reasonable description of a bird population and which exhibits this maximization behaviour when the clutch size is either k or is k or k + 1. Such a model has been suggested by Heyde and Schuh (1978) and it is the object of the present note to indicate how this model may be extended while still retaining the desired characteristic features.