Holmstrom (1982) showed that free-riding is inevitable in partnerships where inputs are substitutes. Legros and Matthews (1993) and Vislie (1994) showed that when inputs are strict complements (Leontief technology), free-riding can be avoided with a linear sharing rule. This paper considers the robustness and some extensions of the positive result of these articles. First, I show that Legros and Matthews's and Vislie's results are not robust to the introduction of participation constraints and limited liability. However, I construct a novel rule that mitigates that problem. Second, I perturb the (deterministic) model of the other authors. It turns out that free-riding is avoidable with noise added to joint output and is inevitable when noise is added to individual productivity. Copyright 2001 by Oxford University Press.