Domain decomposition methods for elliptic problems need a coarse space to be scalable, and there are well established convergence results for these so called two level domain decomposition methods, for both overlapping and non-overlapping subdomains. These results however always contain constants which remain unspecified. I explain in this talk how specific choices of coarse space components can influence these constants. I first show for a simple, one dimensional model problem a coarse space correction which leads together with a Schwarz method to convergence after one coarse correction step; a truly optimal coarse correction. I will then show that such an optimal coarse correction can also be defined for higher dimensional problems, where it however becomes too expensive to be used in practice. I will thus propose approximations of the optimal coarse space, based on multiscale finite element techniques, and show numerical experiments, both for model problems and more realistic high contrast examples.