We have previously presented evidence for a varying fine-structure constant, {alpha}, in two independent samples of Keck/HIRES quasi-stellar object (QSO) absorption spectra. Here we present a detailed many-multiplet analysis of a third Keck/HIRES sample containing 78 absorption systems. We also re-analyse the previous samples, providing a total of 128 absorption systems over the redshift range 0.2<zabs<3.7.