This paper re-visits the smooth sensitivity framework from the point of view of concentrated DP and proposes three new perturbation methods that work under this framework. The results are applied to the problem of estimating the mean of distributions with unbounded support from iid observations, and provide finite-sample bounds on the accuracy. This is a nice fundamental innovation in the theory of DP. When preparing a final version of the manuscript the authors are strongly encouraged to include a discussion about potential further applications of the new mechanisms beyond mean estimation.