PACS. '71.555 -Localization in disordered structures. PACS. 66.301) -Theory of diffusion and ionic conduction in solids.Abstract. -We clarify the validity of the Lifshitz tail for continuous bounded distributions of the random potential in the one-dimensional Anderson model. We find a logarithmic correction in the exponent, heavily affecting the asymptotic long-time behaviour of the return probability in the associated trapping problem.