This paper introduces a new evaluation function, called δ, for the Bandwidth Minimization Problem for Graphs (BMPG). Compared with the classical β evaluation function used, our δ function is much more discriminating and leads to smoother landscapes. The main characteristics of δ are analyzed and its practical usefulness is assessed within a Simulated Annealing algorithm. Experiments show that thanks to the use of the δ function, we are able to improve on some previous best results of a set of well-known benchmarks. Key words: Bandwidth Evaluation Function, Bandwidth Minimization Problem, Heuristics, Simulated Annealing.