Interval narrowing techniques are a key issue for handling constraints over real numbers in the logic programming framework. However, the standard fixpoint algorithm used for computing an approximation of arc consistency may give rise to cyclic phenomena and hence to problems of slow convergence. Analysis of these cyclic phenomena shows: 1) that a large number of operations carried out during a cycle are unnecessary; 2) that many others could be removed from cycles and performed only once when these cycles have been processed. What is proposed here is a revised interval narrowing algorithm for identifying and simplifying such cyclic phenomena dynamically. These techniques are of particular interest for computing stronger consistencies which are often required for a substantial pruning. Experimental results show that such dynamic optimizations improve performance significantly.