Melting in Na_n clusters described with an empirical embedded-atom potential has been reexamined in the size range 55<=n<=147 with a special attention at sizes close to 130. Contrary to previous findings, premelting effects are also present at such medium sizes, and they turn out to be even stronger than the melting process itself for Na_133 or Na_135. These results indicate that the empirical potential is_qualitatively_ unadequate to model sodium clusters.