This paper describes a computational procedure for the determination of complete crystal structures when the cell dimensions and space group only are known from X-ray crystallography. Molecular structure and conformation are assumed, and cannot be refined. When diffraction intensity data are available, the procedure offers an alternative to standard methods for the solution of the phase problem. The procedure applies to a wide range of organic molecules thanks to the evolution of the force field and of the computer programs. While the full ab initio prediction of crystal structures is still, in our opinion, a faraway goal, an important and fruitful application of this kind of computer modeling is in the completion of partial X-ray determinations when single crystals of suitable quality are not available, a rather frequent occurrence. Examples of this application are given, and its success implies that the need for producing good quality single crystals of newly synthesized organic compounds is nowadays less stringent, especially when only a knowledge of the intermolecular organization pattern in the crystal is sought.