Atom-probe tomography is a materials characterization method ideally suited for the investigation of clustering and precipitation phenomena. To distinguish the clusters from the surrounding matrix, the maximum separation algorithm is widely employed. However, the results of the cluster analysis strongly depend on the parameters used in the algorithm and hence, a wrong choice of parameters leads to erroneous results, e.g., for the cluster number density, concentration, and size. Here, a new method to determine the optimum value of the parameter dmax is proposed, which relies only on information contained in the measured atom-probe data set. Atom-probe simulations are employed to verify the method and to determine the sensitivity of the maximum separation algorithm to other input parameters. In addition, simulations are used to assess the accuracy of cluster analysis in the presence of trajectory aberrations caused by the local magnification effect. In the case of Cu-rich precipitates (Cu concentration 40-60 at% and radius 0.25-1.0 nm) in a bcc Fe-Si-Cu matrix, it is shown that the error in concentration is below 10 at% and the error in radius is <0.15 nm for all simulated conditions, provided that the correct value for dmax, as determined with the newly proposed method, is employed.