Abstract The fission cross sections of the symmetric SL-mode and the asymmetric lumped (S1+S2)-mode of the 235U(n, F), 237Np(n, F) and 238U(p, F) reactions are calculated up to E n=200 MeV within a statistical model. For each fissioning nuclide, emerging in (n, xnf) reactions, a separate triaxial outer fission barrier is assumed for the SL-mode. To reproduce the measured branching ratio of symmetric and asymmetric fission events, strong contribution of fission from neutron-deficient nuclei is assumed. Damping of the contribution of triaxial collective modes to the level density at the SL-mode outer saddle seems to be essential for the description of the branching ratio. The sensitivity of the calculated branching ratio to the fissility of the target nuclide and the incident particle is investigated.