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The paper is concerned with a new algorithm (named POSS) for small-sized subset selection based on Pareto optimization. The proposed algorithm is extensively analyzed, compared and tested. A detailed comparison is presented between POSS and the FR algorithm (Forward Regression) for which a theoretical approximation bound is known. The authors also give such a theoretical approximation bound for their algorithm and conclude that POSS does at least as well as the FR algorithm on any sparse regression problem. A second result is given on the exponential decay subclass (a subclass of sparse regression: the observation variables can be ordered in a line such that their covariances are decreasing exponentially with the distance): On this subclass POSS has strictly better guarantees than FR.