Some aspects of the use of symmetry in bifurcation calculations are discussed. First, it is shown how substantial reductions in cost are obtained in computing symmetry-breaking bifurcation points by exploiting the underlying symmetry of a problem. This is demonstrated in a finite-element calculation of 2-dimensional Benard convection in a finite cavity. Second, the stability of paths of symmetry-breaking bifurcation points, which occur when a second parameter in the problem varies, is investigated. A criterion is established for deciding whether intersection of such paths is allowed by symmetry constraints.