In this paper, three approaches are presented for generating and validating sequences of different size neural nets. First, a growing method is given along with several weight initialization methods, and their properties. Then a one pass pruning method is presented which utilizes orthogonal least squares. Based upon this pruning approach, a onepass validation method is discussed. Finally, a training method that combines growing and pruning is described. In several examples, it is shown that the combination approach is superior to growing or pruning alone.