The paper stresses - in sharp contrast with the main contributions in the relevant literature on incomplete contracts - the strategic role of the degree of assets specificity for the enforcement of incomplete contracts. It is shown that under the assumption of endogenous outside options, (i) contractors could maintain strong incentives to make a specific over-investment; (ii) over-investment could act as an endogenous enforcement device. In a bilateral incomplete contract, the rationale for over-investment relies upon the fact that a specific over-investment could lock-in the counterpart into the relationship if it raises the exit costs of the latter by reducing her ex-post outside options. For the same reason, it is shown that a "general purpose" over-investment, could lock-in the counterpart into the relationship if it decreases the exit costs of the investor by increasing his/her ex-post outside options. When outside options are affected by the investments made, each agent tries to reach a monopolistic position by "destroying" his competitors and/or by "encouraging" counterpart competitors. It is then shown that in order to achieve the enforcement of incomplete contracts, specific investments could then provide an optimal enforcement strategy, rather the failure of incomplete contracts. Under the assumption of endogenous outside options, we show that specific investments could increase or decrease counterparts' ex-post outside options, having a strong impact on their incentives to select opportunistic post-contractual behaviour.