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Sensitivity studies of the i process have identified the region around 135I as a bottleneck for the neutron capture flow. Nuclear properties such as the Maxwellian-averaged cross section (MACS) are key to constrain the uncertainties in the final abundance patterns. With the Oslo method, we are able to indirectly measure such properties for the nuclei involved in this process. From the 124Sn(α, pγ)127Sb reaction data we extract the nuclear level density and γ-ray strength function for 127Sb. The level density at higher excitation energies is compatible with the constant-temperature model, while the γ-ray strength function presents features like an upbend and a pygmy-like structure below Sn. From these two quantities we can calculate the MACS for the 126Sb(n, γ)127Sb reaction using the Hauser-Feshbach formalism, and constrain its uncerainties from the theoretical ones. Libraries such as JINA REACLIB, TENDL and BRUSLIB agree well with the experimental results, while ENDF/B-VIII.0 predicts a higher rate. [ABSTRACT FROM AUTHOR]