Structural conditions on polynomial systems are developed for which the Dixon-based resultant methods often compute exact resultants. For cases when this cannot be done, the degree of the extraneous factor in the projection operator computed using the Dixon-based methods is typically minimal. A method for constructing a resultant matrix based on a combination of Sylvester-dialytic and Dixon methods is proposed. A heuristic for variable ordering for this construction often leading to exact resultants is developed.