  Classical estimation techniques for linear models either are inconsistent, or
perform rather poorly, under $\alpha$-stable error densities; most of them are
not even rate-optimal. In this paper, we propose an original one-step
R-estimation method and investigate its asymptotic performances under stable
densities. Contrary to traditional least squares, the proposed R-estimators
remain root-$n$ consistent (the optimal rate) under the whole family of stable
distributions, irrespective of their asymmetry and tail index. While parametric
stable-likelihood estimation, due to the absence of a closed form for stable
densities, is quite cumbersome, our method allows us to construct estimators
reaching the parametric efficiency bounds associated with any prescribed values
$(\alpha_0, \ b_0)$ of the tail index $\alpha$ and skewness parameter $b$,
while preserving root-$n$ consistency under any $(\alpha, \ b)$ as well as
under usual light-tailed densities. The method furthermore avoids all forms of
multidimensional argmin computation. Simulations confirm its excellent
finite-sample performances.
