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We study the problem of differentially private stochastic convex optimization (DP-SCO) with heavy-tailed gradients, where we assume a kth-moment bound on the Lipschitz constants of sample functions rather than a uniform bound. We propose a new reduction-based approach that enables us to obtain the first optimal rates (up to logarithmic factors) in the heavy-tailed setting, achieving error G2⋅1n√+Gk⋅(d√nϵ)1−1k under (ϵ,δ)-approximate differential privacy, up to a mild $$\textup{polylog}(\frac{1}{\delta})$$ factor, where G22 and Gkk are the 2nd and kth moment bounds on sample Lipschitz constants, nearly-matching a lower bound of [Lowy and Razaviyayn 2023]. We further give a suite of private algorithms in the heavy-tailed setting which improve upon our basic result under additional assumptions, including an optimal algorithm under a known-Lipschitz constant assumption, a near-linear time algorithm for smooth functions, and an optimal linear time algorithm for smooth generalized linear models.