  We describe bound states, resonances and elastic scattering of light ions
using a $\delta$-shell potential. Focusing on low-energy data such as energies
of bound states and resonances, charge radii, asymptotic normalization
coefficients, effective-range parameters, and phase shifts, we adjust the two
parameters of the potential to some of these observables and make predictions
for the nuclear systems $d+\alpha$, $\mbox{$^3$He}+\alpha$,
$\mbox{$^3$He}+\alpha$, $\alpha+\alpha$, and $p+\mbox{$^{16}$O}$. We identify
relevant momentum scales for Coulomb halo nuclei and propose how to apply
systematic corrections to the potentials. This allows us to quantify
statistical and systematic uncertainties. We present a constructive criticism
of Coulomb halo effective field theory and compute the unknown charge radius of
$^{17}$F.
