The possibility of deleting a piece of information is very convenient in many programming frameworks. However, this feature is not available in constraint languages such as Constraint Logic Programming or Concurrent Constraint Programming, which allow only for a monotonic accumulation of constraints. This is mainly due to its high complexity and also to its non-monotonic nature, which would make such a system much more complex to reason with. In this paper we consider the CLP framework over FD (finite domain) constraints, and we propose an incremental algorithm which deletes a constraint from a set of FD constraints, while maintaining partial arc-consistency. The algorithm follows the chain of dependencies among variables which are set by the nature of the FD constraints, and by doing so it updates only the part of the constraint set which is affected by the deletion. This makes constraint deletion in FD a feasible task that can be efficiently implemented. 1 Introduction Constraint ...