Damage recovery is critical for autonomous robots that need to operate for a long time without assistance. Most current methods are complex and costly because they require anticipating potential damage in order to have a contingency plan ready. As an alternative, we introduce the T-resilience algorithm, a new algorithm that allows robots to quickly and autonomously discover compensatory behavior in unanticipated situations. This algorithm equips the robot with a self-model and discovers new behavior by learning to avoid those that perform differently in the self-model and in reality. Our algorithm thus does not identify the damaged parts but it implicitly searches for efficient behavior that does not use them. We evaluate the T-resilience algorithm on a hexapod robot that needs to adapt to leg removal, broken legs and motor failures; we compare it to stochastic local search, policy gradient and the self-modeling algorithm proposed by Bongard et al. The behavior of the robot is assessed on-board thanks to an RGB-D sensor and a SLAM algorithm. Using only 25 tests on the robot and an overall running time of 20 min, T-resilience consistently leads to substantially better results than the other approaches.