If only native amplitudes are used for structure determination, then additional 'theoretical' information is necessary to determine their phases. For use in a phasing procedure, this information can be formulated as a selection criterion (figure of merit) which assigns a reliability weight to every trial phase set and distinguishes the closest ones to the true phase set. Different types of additional information may be tested as a selection criterion: electron-density histograms, connectivity properties, statistical likelihood, atomicity etc. A common feature of such criteria is that they do not unambiguously judge the phase quality at low resolution. Nevertheless, the selection of the phase sets with best criterion values increases the ratio of good phase sets in the ensemble considered. An approximate solution of the phase problem may then be found by averaging the selected phase sets. Cluster analysis of the selected phase sets and averaging within clusters allow further improvement of this solution.