Different uncertainty propagation algorithms in graphical structures can be viewed as a particular case of propagation in a joint tree, which can be obtained from different triangulations of the original graph. The complexity of the resulting propagation algorithms depends on the size of the resulting triangulated graph. The problem of obtaining an optimum graph triangulation is known to be NP-complete. Thus approximate algorithms which find a good triangulation in reasonable time are of particular interest. This work describes and compares several heuristic algorithms developed for this purpose.