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When compiling an inventory of hyperdiverse taxa, it is impossible to record the total number of species during fieldwork. To ensure the accuracy of species-richness data it is necessary to assess the reliability of inventories. Accumulation curves are an easy method for doing this and are extensively described in the literature. In this study, we compare the relative fit of various models of species-accumulation functions for six local butterfly inventories, evaluating them by a consideration of the values of the fit, coefficient of determination and sum-of-squares, and the residual patterns and Akaike's Information Criterion. In general, complex functions, such as the Weibull or Chapman-Richards, performed better than simpler and more widely used models (e.g., the Clench and negative exponential models). The performance of models varied among sampling plots, indicating the influence of factors such as land use and community structure. Thus, although the application of more complex models should replace the use of simple ones, further research into the factors affecting model fit of accumulation functions is necessary. [ABSTRACT FROM AUTHOR]