  We make a simple observation that if one of the right-chiral neutrinos is
very heavy or its Yukawa couplings to the standard lepton doublets are
negligible, so that it effectively decouples from the see-saw mechanism, the
prediction for the baryon asymmetry of the Universe resulting from leptogenesis
depends, apart from the masses $M_1$ and $M_2$ of the remaining two
right-chiral neutrinos, only on the element $\YY{22}$ of the neutrino Yukawa
coupling. For $M_2\simgt10M_1$ the lower bound on $M_1$ and also on $T_{\rm
reh}$, resulting from the requirement of 'successful leptogenesis' is then
significantly increased compared to the one computed recently by Buchm\"uller
{\it et al.} in the most general case. Within the framework of thermal
leptogenesis, the only way to lower this limit is then to allow for
sufficiently small mass difference $M_2-M_1$.
