In this article, we explore the contractual design of toll road concession contracts. We highlight the fact that contracting parties try to sign not only complete rigid contracts in order to avoid renegotiations but also flexible contracts in order to adapt contractual framework to contingencies and to create incentives for cooperative behavior. This gives rise to multiple toll adjustment provisions and to a tradeoff between rigid and flexible contracts. Such a tradeoff is formalized using an incomplete contract framework - including ex post maladaptation and renegotiation costs - and propositions are tested using an original database of 71 concession contracts. Our results suggest an important role for economic efficiency concerns, as well as politics, in designing such public-private contracts. Codes JEL : D23, H11, H54, L14, L9.