The Sparse Linear Method (SLIM) is a well-established approach for top-N recommendations. This article proposes several improvements that are enabled by the Alternating Directions Method of Multipliers (ADMM), a well-known optimization method with many application areas. First, we show that optimizing the original SLIM-objective by ADMM results in an approach where the training time is independent of the number of users in the training data, and hence trivially scales to large numbers of users. Second, the flexibility of ADMM allows us to switch on and off the various constraints and regularization terms in the original SLIM-objective, in order to empirically assess their contributions to ranking accuracy on given data. Third, we also propose two extensions to the original SLIM training-objective in order to improve recommendation accuracy further without increasing the computational cost. In our experiments on three well-known data-sets, we first compare to the original SLIM-implementation and find that not only ADMM reduces training time considerably, but also achieves an improvement in recommendation accuracy due to better optimization. We then compare to various state-of-the-art approaches and observe up to 25% improvement in recommendation accuracy in our experiments. Finally, we evaluate the importance of sparsity and the non-negativity constraint in the original SLIM-objective with sub-sampling experiments that simulate scenarios of cold-starting and large catalog sizes compared to relatively small user base, which often occur in practice.