The astrophysical s-process is one of the two main processes forming elements heavier than iron. A key outstanding uncertainty surrounding s-process nucleosynthesis is the neutron flux generated by the 22 Ne(α, n) 25 Mg reaction during the He-core and C-shell burning phases of massive stars. This reaction, as well as the competing 22 Ne(α, γ) 26 Mg reaction, is not well constrained in the important temperature regime from ∼0.2-0.4 GK, owing to uncertainties in the nuclear properties of resonances lying within the Gamow window. To address these uncertainties, we have performed a new measurement of the 22 Ne( 6 Li, d) 26 Mg reaction in inverse kinematics, detecting the outgoing deuterons and 25,26 Mg recoils in coincidence. We have established a new n/γ decay branching ratio of 1.14(26) for the key E x = 11.32 MeV resonance in 26 Mg, which results in a new (α, n) strength for this resonance of 42(11) µeV when combined with the well-established (α, γ) strength of this resonance. We have also determined new upper limits on the α partial widths of neutron-unbound resonances at E x = 11. 112, 11.163, 11.169, and 11.171 MeV. Monte-Carlo calculations of the stellar 22 Ne(α, n) 25 Mg and 22 Ne(α, γ) 26 Mg rates, which incorporate these results, indicate that both rates are substantially lower than previously thought in the temperature range from ∼0.2-0.4 GK.