A minimum principle is proposed which enables problems to be solved involving any form of discontinuity in a structure. This principle is the familiar one of Complementary Energy, but stated in such a way that all problems involving lack-of-fit can be dealt with easily and in a unified manner. Of interest to university teachers is the proof of the minimum complementary energy principle offered in the appendix. It has the advantage over more familiar proofs in that it is completely general and rigorous including non-linear elasticity and discontinuity effects, and yet is short and easily understood. It is therefore very satisfactory for inclusion in a course on structural analysis. Methods are outlined which enable two classes of problems to be solved: (i) solution of stresses in redundant structures, and (ii) the calculation of deflection in structures containing discontinuous strains. The methods are illustrated with three simple examples.