Graph unification is the most expensive part of unification-based grammar parsing. It often takes over 90% of the total parsing time of a sentence. We focus on two speed-up elements in the design of unification algorithms: 1) elimination of excessive copying by only copying successful unifications, 2) Finding unification failures as soon as possible. We have developed a scheme to attain these two elements without expensive overhead through temporarily modifying graphs during unification to eliminate copying during unification. .