Re-writable phase-change memory used in optical storage (e.g. DVD-RAM) is based upon amorphous-crystalline phase changes in chalcogenide alloys of which Ge-Sb-Te are a important example. Ge-Sb-Te alloys that lie along the pseudobinary tie line GeTe-Sb2Te3 are known to exhibit high speed, reversible transitions. We have used x-ray absorption to systematically study the structural changes occurring during the amorphous to crystalline transition in several representative compounds lying on this tie-line including GeTe, Ge2Sb2Te5, and GeSb2Te4. While we find that similar (distorted rocksalt) structures exists for the metastable crystalline phase for all three compounds, we find for the amorphous phases that the bonds grow shorter and stronger with the coordination for each atom type reverting towards the local coordination predicted by the 8-N rule. The amorphous structure in each case is characterized by a switch of Ge from a nearly octahedral position to a tetrahedrally coordinated position.