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In this paper we investigate convergence of Landweber iteration in Hilbert scales for linear and nonlinear inverse problems. As opposed to the usual application of Hilbert scales in the framework of regularization methods, we focus here on the case s 0, which (for Tikhonov regularization) corresponds to regularization in a weaker norm. In this case, the Hilbert scale operator L2s appearing in the itera-tion acts as a preconditioner, which signicantly reduces the number of iterations needed to match a stopping criterion. Additionally, we carry out our analysis un-der signicantly relaxed conditions, i.e., we only require kTxk mkxka instead of kTxk kxka, which is the usual condition for regularization in Hilbert scales. The assumptions needed for our analysis are veried for several examples and numerical results are presented conrming the theoretical ones.