  We consider leptogenesis induced by soft supersymmetry breaking terms ("soft
leptogenesis"), in the context of the inverse seesaw mechanism. In this model
there are lepton number (L) conserving and L-violating soft
supersymmetry-breaking B-terms involving the singlet sneutrinos which, together
with the -- generically small-- L-violating parameter responsible of the
neutrino mass, give a small mass splitting between the four singlet sneutrino
states of a single generation. In combination with the trilinear soft
supersymmetry breaking terms they also provide new CP violating phases needed
to generate a lepton asymmetry in the singlet sneutrino decays. We obtain that
in this scenario the lepton asymmetry is proportional to the L-conserving soft
supersymmetry-breaking B-term, and it is not suppressed by the L-violating
parameters. Consequently we find that, as in the standard see-saw case, this
mechanism can lead to sucessful leptogenesis only for relatively small value of
the relevant soft bilinear coupling. The right-handed neutrino masses can be
sufficiently low to elude the gravitino problem. Also the corresponding Yukawa
couplings involving the lightest of the right-handed neutrinos are constrained
to be \sum |Y_{1k}|^2\lesssim 10^{-7} which generically implies that the
neutrino mass spectrum has to be strongly hierarchical.
