  The microscopic studies on nuclear fission require the evaluation of the
potential energy surface as a function of the collective coordinates. A
reasonable choice of constraints on multipole moments should be made to
describe the topography of the surface completely within a reasonable amount of
computing time. We present a detailed analysis of fission barriers in the
self-consistent Hartree-Fock-Bogoliubov approach with the D1S parametrization
of the Gogny nucleon-nucleon interaction. Two heavy isotopes representing
different spontaneous fission modes - $^{252}$Cf (asymmetric) and $^{258}$No
(bimodal) - have been chosen for the analysis. We have shown the existence of
complicated structures on the energy surface that can not be fully described in
two-dimensional calculations. We analyze apparent problems that can be
encountered in this type of calculations: multiple solutions for given
constraints and transitions between various potential energy surfaces. We
present possible solutions on how to deal with these issues.
