Model-observation comparisons of type-I X-ray bursts (XRBs) can reveal the properties of accreting neutron star systems, including the neutron star compactness. XRBs are powered by nuclear burning, and a handful of reactions have been shown to impact the model results. Reactions in the NiCu cycles, featuring a competition between⁵⁹Cu(p,γ)⁶⁰Zn and⁵⁹Cu(p,α)⁵⁶Ni, have been shown to be among the most important reactions as they are a critical checkpoint inrp-process flow and significantly impact the light curves and burst ashes. We report a direct measurement of⁵⁹Cu(p,α)⁵⁶Ni, bringing stringent constraints on this reaction rate. New results rule out a strong NiCu cycle in XRBs, with a negligible degree of recycling, ≤5% up to 1.5 GK. The new reaction rate, when varied within new uncertainty limits, shows no impact on one-zone XRB model light curves tailored for clocked-bursterGS1826–24, hence removing an important nuclear physics uncertainty in the model-observation comparison.