The 12Cðα; γÞ16O reaction plays a central role in astrophysics, but its cross section at energies relevant for astrophysical applications is only poorly constrained by laboratory data. The reduced α width, γ11, of the bound 1− level in 16O is particularly important to determine the cross section. The magnitude of γ11 is determined via sub-Coulomb α-transfer reactions or the β-delayed α decay of 16N, but the latter approach is presently hampered by the lack of sufficiently precise data on the β-decay branching ratios. Here we report improved branching ratios for the bound 1− level [bβ;11 ¼ ð5.02 0.10Þ × 10−2] and for β-delayed α emission [bβα ¼ ð1.59 0.06Þ × 10−5]. Our value for bβα is 33% larger than previously held, leading to a substantial increase in γ11. Our revised value for γ11 is in good agreement with the value obtained in α-transfer studies and the weighted average of the two gives a robust and precise determination of γ11, which provides significantly improved constraints on the 12Cðα; γÞ cross section in the energy range relevant to hydrostatic He burning.