In this paper we combine the approaches from [21] and [11] for approximating global attractors. In [21] the global attractors is arbitrarily well approximated by sets that are not necessarily positively invariant. On the contrary, the method from [11] provides supersets of the global attractor which are positively invariant but not necessarily converging. In this paper we marry both approaches by combining their techniques and get converging outer approximations of the global attractor consisting of positively invariant sets. Because both the methods from [21] and [11] are based on convex optimization via sum-of-squares techniques the same is true for our proposed method. The method is easy to use and numerical examples illustrate the procedure.