This paper introduces Twist-routing, a new routing algorithm for faulty on-chip networks, which improves Maze-routing, a face-routing based algorithm which uses deflections in routing, and archives full fault coverage and fast packet delivery. To build Twist-routing algorithm, we use bounding circles, which borrows the idea from GOAFR+ routing algorithm for ad-hoc wireless networks. Unlike Maze-routing, whose path length is unbounded even when the optimal path length is fixed, in Twist-routing, the path length is bounded by the cube of the optimal path length. Our evaluations show that Twist-routing algorithm delivers packets up to 35% faster than Maze-routing with a uniform traffic and Erdös-Rényi failure model, when the failure rate and the injection rate vary.