In this paper, the parallelization of parallel independent rule applications within the double-pushout approach over adhesive categories is generalized in such a way that doubling can be avoided. If two rule applications to the same object delete the same part of the commonly accessed part, then independence is restored by removing the deletion part of one of the rule applications. Similarly, one can avoid that certain insertions are doubled. It turns out that parallelization with doubling avoidance is closely related to synchronization by means of amalgamated rules.