  We prove that the Weyl function of the one-dimensional Dirac operator on the
half-line $\mathbb{R}_+$ with exponentially decaying entropy extends
meromorphically into the horizontal strip $\{0\ge \mbox{Im}\,z > -\delta\}$ for
some $\delta > 0$ depending on the rate of decay. If the entropy decreases very
rapidly then the corresponding Weyl function turns out to be meromorphic in the
whole complex plane. In this situation we show that poles of the Weyl function
(scattering resonances) uniquely determine the operator.
