In this paper, we propose a procedure to accelerate the resolu- tion of the well-known “Elastic-Net” problem. Our procedure is based on the (partial) identification of the solution support and the reformulation of the original problem into a problem of reduced dimension. The identification of the support lever- ages the novel concept of “safe relaxing” where one aims to identify non-zero coefficients of the solution. It can be viewed as a dual approach to “safe screening“ introduced in the last decade and allowing to reduce the problem dimension using the identification of zero coefficients of the solution. We show numerically that combining both methodologies in a “Screen & Relax” strategy enables to significantly improve the trade- off between complexity and accuracy achievable by standard resolution techniques.