Addendum to: "Lifting smooth curves over invariants for representations of compact Lie groups, III" [J. Lie Theory 16 (2006), No. 3, 579-600.]

We improve the main results in the paper from the title using a recent refinement of Bronshtein's theorem due to Colombini, Orr\'u, and Pernazza. They are then in general best possible both in the hypothesis and in the outcome. As a consequence we obtain a result on lifting smooth mappings in several variables.