  In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$
and a two-sided bound for the integrated density of states $N(E)$ at an
arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension.
These Schr\"odinger operators are given by potentials of identical shape
centered at every lattice site but with non-overlapping supports and with
randomly varying coupling constants. Both types of bounds only involve
scattering data for the single-site potential. They show in particular that
both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like
$1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.
