Neutron-diffraction data have been obtained from CoO single crystals, cooled down through the N\'eel point, while applying a small pressure. Thus, crystallographically almost untwinned, tetragonal crystals were obtained. The observed intensities can be explained either by the collinear-spin model given by Roth, with the assumption that any of the four possible antiferromagnetic domains occurs with exactly the same volume, or by the multi-spin-axis model proposed by van Laar. The results are compared with magnetic-torque measurements.