  Probability of reflection $R(E)$ off a finite attractive scattering potential
at zero or low energies is ordinarily supposed to be 1. However, a fully
attractive potential presents a paradoxical result that $R(0)=0$ or $R(0)<1$,
when an effective parameter $q$ of the potential admits special discrete
values. Here, we report another class of finite potentials which are
well-barrier (attractive-repulsive) type and which can be made to possess much
less reflection at zero and low energies for a band of low values of $q$. These
well-barrier potentials have only two real turning points for $E \in(V_{min},
V_{max})$, excepting $E=0$. We present two exactly solvable and two numerically
solved models to confirm this phenomenon.
