  The first terms of the low-signal-energy asymptotics for the mutual
information in the discrete-time Poisson channel are derived and compared to an
asymptotic expression of the capacity. In the presence of non-zero additive
noise (either Poisson or geometric), the mutual information is concave at zero
signal-energy and the minimum energy per bit is not attained at zero capacity.
Fixed signal constellations which scale with the signal energy do not attain
the minimum energy per bit. The minimum energy per bit is zero when additive
Poisson noise is present and $\ew\log 2$ when additive geometric noise of mean
$\ew$ is present.
