  This work studies the secrecy-capacity of a scalar-Gaussian wiretap channel
with an amplitude constraint on the input. It is known that for this channel,
the secrecy-capacity-achieving distribution is discrete with finitely many
points. This work improves such result by showing an upper bound of the order
$\frac{\mathsf{A}}{\sigma_1^2}$ where $\mathsf{A}$ is the amplitude constraint
and $\sigma_1^2$ is the variance of the Gaussian noise over the legitimate
channel.
