We investigate fault-tolerant routing which aims at finding feasible minimum paths in a faulty hypercube. The concept of unsafe node and its extension are used in our scheme. A set of stringent criteria is proposed to identify the possibly bad candidates for forwarding a message. As a result, the number of such undesirable nodes is reduced without sacrificing the functionality of the mechanism. Furthermore, the notion of degree of unsafeness for classifying the unsafe nodes is introduced to facilitate the design of efficient routing algorithms which rely on having each node keep the states of its nearest neighbors. We show that a feasible path of length no more than the Hamming distance between the source and the destination plus four can always be established by the routing algorithm as long as the hypercube is not fully unsafe. The issue of deadlock freeness is also addressed in this research. More importantly, another fault-tolerant routing algorithm, which requires only a constant of five virtual networks in wormhole routing to ensure the property of deadlock freeness for a hypercube of any size, is presented in this paper.