Sightings of any member of a population of unknown sizeNoccur according to a homogeneous Poisson process. The processes are independent and have a common rate. Individuals are given a distinctive tag at the time they are first sighted. Various stopping rules have appeared in different areas of the literature for deciding when all the individuals in the population have been seen. The average time to termination of these rules is compared. Computational results suggest that the best performances are provided by two of the rules based on the cumulative waiting time to sight a given number of unmarked individuals