In this paper we compare nested dissection orderings obtained by different graph bisection heuristics. In the context of parallel sparse matrix factorization the quality of an ordering is not only determined by its fill reducing capability, but also depends on the difficulty with which a balanced mapping of the load onto the processors of the parallel computer can be found. Our analysis shows that sophisticated local bisection heuristics combined with the multilevel method result in high quality orderings. Furthermore, these orderings can be computed in a reasonable amount of time.