[en] We present a new rearrangement of short-range interactions in the ¹S₀ nucleon-nucleon channel within chiral effective field theory. This is intended to address the slow convergence of Weinberg’s scheme, which we attribute to its failure to reproduce the amplitude zero (scattering momentum ≃340 MeV) at leading order. After the power counting scheme is modified to accommodate the zero at leading order, it includes subleading corrections perturbatively in a way that is consistent with renormalization-group invariance. Systematic improvement is shown at next-to-leading order, and we obtain results that fit empirical phase shifts remarkably well all the way up to the pion-production threshold. As a result, an approach in which pions have been integrated out is included, which allows us to derive analytic results that also fit phenomenology surprisingly well.