In circuit-switched routing, the path between a source and its destination is established by incrementally reserving all required links before the data transmission can begin. If the routing algorithm is not carefully designed, deadlocks can occur in reserving these links. Deadlock-free algorithms based on dimension-ordered routing, such as the E-cube , exist. However, E-cube does not provide any flexibility in choosing a path from a source to its destination and can thus result in long latencies under heavy or uneven traffic. Adaptive, minimum-distance routing algorithms, such as the Turn Model and the UP Preference algorithms, have previously been reported. In this article, we present a new class of adaptive, provably deadlock-free, minimum-distance routing algorithms. We prove that the algorithms developed here are optimally adaptive in the sense that any further flexibility in communication will result in deadlock. We show that the Turn Model is actually a member of our new class of algorithms that does not perform as well as other algorithms within the new class. It creates artificial hotspots in routing the traffic and allows fewer total paths. We present an analytical comparison of the flexibility and balance in routing provided by various algorithms and a comparison based on uniform and nonuniform traffic simulations. The Extended UP Preference algorithm developed in this article is shown to have improved performance with respect to existing algorithms. The methodology and the algorithms developed here can be used to develop routing for other schemes such as wormhole routing, and for other recursively defined networks such as k -ary n -cubes.