  A model in which a gap forms in the renormalized electronic density of state
(DOS) with missing states recovered just above the pseudogap $\Delta_{pg}$, is
able to give a robust description of the striking, triangular like, peak seen
in the real part of the optical self-energy of underdoped cuprates. We use this
model to explore the effect of the pseudogap on the real part of the optical
conductivity and on the partial sum rule associated with it. An important
result is that the optical spectral weight redistributes over a much larger
frequency window than it does in the DOS.
