We have used first-principles variable-cell-shape dynamics to investigate the compressive behavior of ice XI and ice VIII. We have observed direct reconstructions between these prototypical low and high density phases, in both directions. These transformations are not observed in practice, instead both forms amorphize under (de)compression. From this perspective, the amorphous can be viewed as an intermediate step in the low <-> high density transformations. The reconstruction paths we observe bypass the intermediate amorphous phases and preserve the style of dipole ordering of the parent structure leading to metastable phases and large hystereses. (c) 2005 Elsevier B.V. All rights reserved.