  Bayesian, classical, and extended maximum likelihood approaches to estimation
of upper limits in experiments with small numbers of signal events are
surveyed. The discussion covers only experiments whose outcomes are well
described by a Poisson statistic. A new approach, based on the statistical
significance of a signal rather than on the number of events in the signal
region, is proposed. A toy model and an example of a recent search for the
lepton number violating decay $\tau\to\mu\gamma$ are used to illustrate
application of the discussed techniques.
