  We show that a relative entropy condition recently shown by Leger and Vasseur
to imply uniqueness and stable $L^2$ dependence on initial data of Lax 1- or
$n$-shock solutions of an $n\times n$ system of hyperbolic conservation laws
with convex entropy implies Lopatinski stability in the sense of Majda. This
means in particular that Leger and Vasseur's relative entropy condition
represents a considerable improvement over the standard entropy condition of
decreasing shock strength and increasing entropy along forward Hugoniot curves,
which, in a recent example exhibited by Barker, Freist\"uhler and Zumbrun, was
shown to fail to imply Lopatinski stability, even for systems with convex
entropy. This observation bears also on the parallel question of existence, at
least for small $BV$ or $H^s$ perturbations
