The structure of human rhinovirus 14 has been refined, by the method of restrained least squares, to an R factor of 0.16 for various random samples between 6 and 3 A resolution with F greater than 3 sigma (F). As a first step the non-crystallographic symmetry parameters were optimized using the initial atomic model in a rigid-body refinement procedure. Phase determination by the molecular-replacement phase extension and refinement procedure was continued to 2.94 A resolution, employing the improved non-crystallographic symmetry operators. The resultant structure-factor phases and weights, together with the measured amplitudes, constituted the X-ray observations used in the restrained refinement. The Hendrickson-Konnert program system [Konnert & Hendrickson (1980). Acta Cryst. A36, 344-350] was modified to incorporate non-crystallographic symmetry constrains and structure-factor phases as observations. The non-bonded contacts between subunits related by non-crystallographic symmetry were also restrained.