The author considers the so called ``rejection technique'', sometimes used in the practice of Monte Carlo methods. It consists substantially in evaluating the area of a surface contained in a domain suitably defined utilizing the percentage of the random points of a sequence equidistributed in the domain that hits the surface. Many problems can easily be reduced to this scheme but it is well known that such procedure can lead to considerable errors. In this paper the author takes again this topic and illustrates two examples (concerning the calculation of an integral and the generation of random points with an assigned distribution) in which the efficiency of this technique compared with the crude Monte Carlo can assume values arbitrarily small.