A toroidal field coil for a small aspect ratio, high field tokamak Ignition Test Reactor was designed based on compound constant tension coil shapes. Finite element analyses revealed the existence of bending stresses in this coil due to incompatible deformations of the different constant tension shapes at their common joining points. To correct this situation, the deformation equations of constant tension coils were derived and solved analytically. This permitted selection of cross-sectional dimensions for each coil segment that gave compatible deformations and no bending moments at the joining points. Zero moment theory for compound coils was then extended considering nonuniform continuous elastic coil support effects in the governing equations. Analytical and numerical results were obtained for this case as well.