usual nonparametric rate in (ordinary) function spaces. For example, as demonstrated in Zinde-Walsh (2008) kernel estimators of density that may diverge if the distribution function is not absolutely continuous, are always (under the usual assumptions on kernel/bandwidth) consistent in the weak topology of the space of generalized functions, where the density problem is well-posed. Here, well-posedness holds for deconvolution as long as the error density is not super-smooth. When well-posedness cannot be ensured, plug-in estimation will not provide consistent results and some regularization is required; usually spectral cut-off is employed for the problems considered here. In the context of these non- parametric models regularization requires extra information: the knowledge of the rate of decay of the Fourier transform of some of the functions. For model 1 this is not a problem since φ$_{u}$ is assumed known; the regular- ization uses the information about the decay of this characteristic function to construct a sequence of compactly supported solutions with support increas- ing at a corresponding rate. In S ∗ no regularization is required for plug-in estimation unless the error distribution is super-smooth. Exponential growth in φ − 1 u provides a logarithmic rate of convergence in function classes for the estimator (Fan, 1991). Below we examine spectral cut-off regularization for the deconvolution in S ∗ when the error density is super-smooth. With super-smooth error in S ∗ define a class of generalized functions 50 5.2 Regularization in plug-in estimation