Constraint relaxation is the modi® cation of a constraint network such that the network permits more solutions ; for instance, a formerly inconsistent network may become consistent. M ost of the algorithms in this area try to localize constraints or even whole levels (of priority) of constraints that must be removed to allow global consistency. However, the problem when removing entire (levels of) constraints is the high degree of violation of the original problem. (It is often the case that constraints do not permit only a few tuples which are essential to form a globally consistent solution. Removing whole (levels of) constraints is much farther away from the original problem than additionally permitting just the necessary tuples.) Th e present approach does not work on a constraint level, but on a tuple level. Th is greatly reduces the distance of the modi® ed (relaxed) problem from the original (hard) one. In this paper an`intelligent' approach is pursued where only the constraints explicitly given are considered ; therefore, no redundant constraints are synthesized. Furthermore, only that part of the constraint network that is actually aOE ected by the modi® cations is recomputed which is especially eOE ective in the frequent cases when only a few tuples are changed.