Abstract Methods have been proposed to construct compensators for irregular body contours and oblique beam incidence. In the former case a compensator can be constructed in a single piece, provided a suitable material of reduced density (to compensate for reduction in scattered radiation) is used. Suitable density factors were determined for various mounting distances of a compensator. The use of brass compensating wedges was suggested, specifically for radiation beams incident obliquely on a flat surface. The correction factors for beam divergence and reduction in scatter were incorporated in the calculation of wedge angles.