  Two systematic sources of error in most current microscopic evaluations of
fission-barrier heights are studied. They are concerned with an approximate
treatment of the Coulomb exchange terms (known as the Slater approximation) in
the self-consistent mean fields and the projection on good parity states (e.g.,
of positive parity for the spontaneous fission of an even-even nucleus) of
left-right reflection asymmetric intrinsic solutions (e.g., around the second
barrier). Approximate or unprojected solutions are shown to lead each to an
underestimation of the barrier heights by a few hundred keV.
