We have previously proposed a method for preparing dense amorphous polymer samples which was designed to circumvent the need for long periods of relaxation to equilibrium [J. I. McKechnie, D. Brown, and J. H. R. Clarke, Macromolecules 25, 1562 (1992)]. In the current article, we examine in more detail the application of the method to the preparation of polymer melts using precise data from massively parallel simulations. We expose deficiencies in the original method and introduce a modification which improves the equilibration. The limitations of the overall procedure are discussed in detail.