  We consider the possibility that a light sterile-neutrino species $\nu_S$ can
be produced by $\nu_e$ scattering during the cooling of a proto-neutron star.
If we parameterize the sterile neutrino production cross-section by a parameter
$A$ as $\sigma (\nu_e X\rightarrow \nu_S X) = A \sigma(\nu_e X\rightarrow \nu_e
X)$, where $X$ is an electron, neutron or proton, we show that $A$ is
constrained by limits to the conversion of $\nu_e$ to $\nu_S$ in the region
between the sterile-neutrino trapping region and the electron-neutrino trapping
region. This consideration excludes values of $A$ in the range between $10^{-4}
\la A \la 10^{-1}$.
