This paper describes a computer program, for evaluating the tolerance range to be assigned to each parameter of an optical system, when the perform ance specifications are given. The results obtained are not statistical, that is if all parameters are within their computed ranges, it is certain, not probable, that the optical system perform ance is with in specifications. The process is iterative. A very small alteration is assigned to each parameter, and the resulting wave front alteration is evaluated. During the first scanning and for each parameter, the program chooses the directions of alteration causing the greater worsening effect on the wavefront. These directions are kept fixed during all the subsequent scannings. After each scanning, the performances of the modified optical system are checked to be within specifications. If so, a new scanning process starts. The iterative search ends when either suitable boundary conditions are reached, or the system performances exceed the specifications. In both cases, one of the two tolerance limits for each involved parameter is obtained. The other limit is computed by returning the program to the starting system, and repeating the procedure with all the directions of the parameter variations reversed. The validity of the method is based on the assumption that each alteration is so small, that, within the same scanning, it does not appreciably change the effect on the wavefront of the subsequent parameter variations.