Information on ground-dwelling arthropod densities is important for efficient management in agro-ecosystems. A method of using paired pitfall traps with different inter-trap distances, called the two-circle method (TCM), was proposed recently for accurate and efficient estimation of arthropod densities. Using the numbers of individuals caught in paired traps and the inter-trap distances between the paired traps as input, the TCM can simultaneously estimate the effective trapping radius and the population density by fitting a nonlinear model. However, the previous fitting procedure (using the nonlinear least squares approach) provides the estimates and standard errors of only these two variables, and often suffers from its hypersensitivity to the initial values assigned in the nonlinear regression. To estimate the confidence intervals of these estimates and to assess the effects of the number of replications per distance class and the number of distance classes on the accuracy of density estimates, we provide a new procedure for fitting the model by using the optimization function. Evaluation based on simulated and field data suggests that the TCM could provide a reliable estimate of density by using at least 15 paired traps per distance class and at least 4 distance classes.