  In the context of GUT baryogenesis models, a well-known theorem asserts that
CPT conservation and the unitarity of S-matrix require that the lowest order
contribution that leads to the generation of a non-zero net CP-violation via
the decay of a heavy particle must be to $\mathcal{O}({\alpha_\slashed{B}}^3)$,
where $\alpha_\slashed{B}$ is a baryon number (B) violating coupling. We
revisit this theorem (which holds for lepton number (L) violation, and hence
for leptogenesis as well) and examine its implications for models where the
particle content allows the heavy particle to also decay via modes which
conserve B (or L) in addition to modes which do not. We systematically expand
the S-matrix order by order in B\slash L-violating couplings, and show, in such
cases, that the net CP-violation is non-zero even to
$\mathcal{O}({\alpha_\slashed{B}}^2)$, without actually contradicting the
theorem. By replacing a B/L violating coupling (usually constrained to be
small) by a relatively unconstrained B/L conserving one, our result may allow
for sufficient CP violation in models where it may otherwise have been
difficult to generate the observed baryon asymmetry. As an explicit application
of this result, we construct a model in low-scale leptogenesis.
