Abstract The uniqueness type system and lazy graph copying are important techniques to efficiently implement functional languages. Unfortunately combination of both in one system may lead to conflicts. Until recently, parallel Concurrent Clean programs could not take advantage of the uniqueness type system, because the lazy graph copying method that Concurrent Clean employed was able to invalidate derived uniqueness information. This paper will address this problem and present a solution that is based on a new copying method with different semantics, called lazy normal form copying.