We first present a generic pruning technique, which aggregates several constraints sharing some variables. The method is derived from an idea called sweep, which is extensively used, in computational geometry. A first benefit of this technique comes from the fact that it can be applied on several families of global constraints. A second main advantage is that it does not lead to any memory consumption problem since it only requires temporary memory that can be reclaimed after each invocation of the method. We then specialise this technique to the non-overlapping rectangles constraint, describe several optimisations, and give an empirical evaluation based on six sets of test instances with different characteristics.