A heuristic planning procedure allowing to obtain a 3-dimensional conformal dose distribution for target volumes with concavities has been investigated. The procedure divides the planning problem into a number of sub-problems each solvable by known methods. By patching together the solutions to the sub-problems, a solution with a predictable dosimetric outcome can be obtained. The procedure can be applied to most 3-dimensional systems. The procedure is described and its applications to the irradiation of neoplasms are discussed. (A.S.).