Melting in Na-n clusters described with an empirical embedded-atom potential has been reexamined in the size range 55less than or equal tonless than or equal to147 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 inadequate to model sodium clusters. (C) 2004 American Institute of Physics.