The fractionator is illustrated by means of a biomedical example involving the estimation of the number of lymphatic valves in lungs of infants who had died from sudden infant death syndrome (SIDS) and other known causes. The method is unbiased irrespective of tissue deformations and it does not require external information such as section thickness. An upper bound of the coefficient of error of the estimate of the number of valves within one lung was 6.5%, despite the fact that the number of valves counted per lung at the last stage ranged between 11 and 37 only. The upper bound includes the biological variation of the number of valves among infant lungs. Some theoretical remarks are also made on the efficiency of the fractionator. It is suggested, for instance, that the initial sampling stages cause more impact on the precision of the final estimator than the subsequent stages, and that an optimal arrangement of fragments submitted to systematic sampling should have the smallest fragments at the ends, with fragment contents increasing smoothly toward the middle of the series.