The device of split-plot confounding for introducing additional factors into a field experiment can only give a balanced design when the number of whole plots per block and the number of replications of each whole-plot treatment are multiples of the number of sub-sets into which the combinations of the additional factors are divided. When this condition is not satisfied it may still be possible to arrange that the design shall be partially or nearly balanced in such a way as to be useful in practice and to require a reasonably simple statistical analysis. Nevertheless, the experimenter should always bear in mind the desirability of balance, and should have recourse to unbalanced designs only when the exigencies of space or material, or an unforeseen necessity of introducing extra factors during the course of an experiment, leave him with no alternative. No attempt has been made to give a comprehensive account of designs of this kind, but the numerical analysis of the yields from a typical experiment has been discussed in detail. Though the lack of balance leads to some non-orthogonality of treatment contrasts, the more important comparisons can usually be satisfactorily estimated. The details of this estimation vary from one experiment to another, but the example given should make the principles clear to those who are familiar with the analysis of variance. I am indebted to Dr E. M. Crowther and to the Agricultural Research Council for permission to use the numerical results discussed in this paper