We consider the mean-variance portfolio selection problem with the added requirement of choosing a restricted number of assets to be included in the optimal portfolio. The resulting problem is non-convex and non-differentiable to the presence of the L0-norm. A study of local and global minimizers is undertaken for the cases : (1) without a riskless asset and (2) in the presence of a riskless asset. Based on the results, an implicit enumeration algorithm coupled with an elimination heuristic is developed and tested on real instances. Results are benchmarked against a state-of-the-art commercial solver to which a MIP formulation of the problem is input. Joint work with Buse Şen (EPFL) and Deniz Akkaya (Bilkent Univ.)