A previous study showed that the diffraction from cubic crystals of an icosahedral virus, cowpea mosaic virus (CPMV), was dramatically improved under elevated hydrostatic pressure. This use of pressure may have a significant impact on structural biology if it is found to be generally applicable. There were two types of cubic crystals assigned in either an I23 or P23 space group. They show the same rhombic dodecahedral morphology at atmospheric pressure. The crystals assigned to the I23 space group diffracted X-rays to higher resolution than those with P23 space group. The assignment of P23 space group was owing to the presence of reflections with indices of h + k + l = (2n + 1) (odd reflections), which are forbidden in space group I23. Analysis of the odd reflections from the P23 crystals at atmospheric pressure showed that they can originate from a rotational disorder in the I23 crystals. The odd reflections were eliminated with the application of 3.5 kbar of pressure, which transformed the crystals from the apparently primitive cell to the body-centered I23 space group with dramatic improvement in diffraction. A mechanistic model is proposed to describe the induction of order by rectifying the imperfection, which is consistent with the experimental data.