Summary • Several species richness estimators (two non-parametric, four based on rarefaction curves and two from fitting of abundance distributions) were compared by examining their performance in estimating the species richness for two moth data sets from the United Kingdom. Comparisons were also made using data simulated from the fitted abundance distributions. • The different species richness estimators gave different estimates. The non-parametric estimates and the rarefaction estimates were similar, but were smaller than the parametric estimates. When the simulated data were used, the only methods to give estimates near the true value was the parametric method using the distribution from which the data were simulated. • At present it is impossible to decide whether any of the estimation methods will give a realistic estimate, as not enough is known about the true numbers of species in communities. Until this is rectified, the most that can be hoped for is to obtain upper and lower bounds on species richness. Journal of Animal Ecology (2005) 74, 375 –386 doi: 10.1111/j.1365-2656.2005.00940.x