Perfect simulation of a one-dimensional loss network on R with length distribution pi and cable capacity C is performed using the clan of ancestors method. Previous works estimated the region of convergence of this scheme using a domination by a branching process. In this work, we show that the domination by the branching process is far from sharp and that there is room for improvement. Moreover, we derive an empirical relation concerning the critical value using simulation studies on the number of rectangles present in the clan of ancestors.103453469