The Littlest Seesaw (LS) model involves two right-handed neutrinos and a very constrained Dirac neutrino mass matrix, involving one texture zero and two independent Dirac masses, leading to a highly predictive scheme in which all neutrino masses and the entire PMNS matrix is successfully predicted in terms of just two real parameters. We calculate the renormalisation group (RG) corrections to the LS predictions, with and without supersymmetry, including also the threshold effects induced by the decoupling of heavy Majorana neutrinos both analytically and numerically. We find that the predictions for neutrino mixing angles and mass ratios are rather stable under RG corrections. For example we find that the LS model with RG corrections predicts close to maximal atmospheric mixing, theta(23) = 45 degrees +/- 1 degrees, in most considered cases, in tension with the latest NOvA results. The techniques used here apply to other seesaw models with a strong normal mass hierarchy.