Set membership identification seeks to obtain models amenable to be used in a robust control framework. While under suitable assumptions this problem is convex, existing methods lead to high order models. As we show in this note, this difficulty can be avoided by recasting the problem as a structured nuclear norm minimization. To solve this problem, we propose a computationally efficient first order algorithm that requires performing only a combination of thresholding and eigenvalue decomposition steps. Finally, since the optimization is carried out only over sequences compatible with the output responses of stable systems, the identified model is guaranteed to be stable.