Abstract When attempting fission-track age estimation of young deposits, it may happen that only a small number of spontaneous tracks are observed. If no tracks are recorded, the only age-related quantity which can be calculated is a conservative upper confidence bound. Both upper and lower confidence bounds can be calculated if one or more spontaneous tracks are observed. However, for small track numbers the lower bound will be near the absolute bound of age zero, thus providing minimal information. In this situation, it is more useful to calculate a single upper confidence bound for the true age. Some simple formulae are given for the calculation of the confidence bounds for the particular case where the neutron dose is known.