We consider regret minimization in adversarial deterministic Markov Decision Processes (ADMDPs) with bandit feedback. We devise a new algorithm that pushes the state-of-theart forward in two ways: First, it attains a regret of O(T 2/3 ) with respect to the best fixed policy in hindsight, whereas the previous best regret bound was O(T 3/4 ). Second, the algorithm and its analysis are compatible with any feasible ADMDP graph topology, while all previous approaches required additional restrictions on the graph topology.