  We prove explicit asymptotics for the location of semiclassical scattering
resonances in the setting of $h$-dependent delta-function potentials on
$\mathbb{R}$. In the cases of two or three delta poles, we are able to show
that resonances occur along specific lines of the form $\Im z \sim -\gamma h
\log(1/h).$ More generally, we use the method of Newton polygons to show that
resonances near the real axis may only occur along a finite collection of such
lines, and we bound the possible number of values of the parameter $\gamma.$ We
present numerical evidence of the existence of more and more possible values of
$\gamma$ for larger numbers of delta poles.
