We calculate fission barriers with the Skyrme‐Hartree‐Fock‐Bogoliubov plus particle number projection (SHFB+PLN) method, using a Skyrme force fitted to essentially all the nuclear mass data with the same method. The reflection asymmetry is introduced to study the lowering of the outer barrier of three selected nuclei. We discuss the feasability of performing large‐scale SHFB+PLN fission‐barrier calculations, i.e. for about 2000 nuclei of astrophysical interest. © 2004 American Institute of Physics