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Ordered distance sampling is a point-to-object sampling method that can be labor-efficient for demanding field situations. An extensive simulation study was conducted to find the optimum number, g, of population members to be encountered from each random starting point in ordered distance sampling. Monte Carlo simulations covered 64 combinations of four spatial patterns, four densities and four sample sizes. Values of g from 1 to 10 were considered for each case. Relative root mean squared error (RRMSE) and relative bias were calculated for each level of g, with RRMSE used as the primary assessment criterion for finding the optimum level of g. A nonparametric confidence interval was derived for the density estimate, and this was included in the simulations to gauge its performance. Superior estimation properties were found for g > 3, but diminishing returns, relative to the potential for increased effort in the field, were found for g > 5. The simulations showed noticeable diminishing returns for more than 20 sampled points. The non-parametric confidence interval performed well for populations with random, aggregate or double-clumped spatial patterns, but rarely came close to target coverage for populations that were regularly distributed. The non-parametric confidence interval presented here is recommended for general use. Published in 2004 by John Wiley & Sons, Ltd.