In this paper we present a methodology to design fault-tolerant routing algorithms for regular direct interconnection networks. It supports fully adaptive routing, does not degrade performance in the absence of faults, and supports a reasonably large number of faults without significantly degrading performance. The methodology is mainly based on the selection of an intermediate node (if needed) for each source-destination pair. Packets are adaptively routed to the intermediate node and, at this node, without being ejected, they are adaptively forwarded to their destinations. In order to allow deadlock-free minimal adaptive routing, the methodology requires only one additional virtual channel (for a total of three), even for tori. Evaluation results for a 4x4x4 torus network show that the methodology is 5-fault tolerant. Indeed, for up to 14 link failures, the percentage of fault combinations supported is higher than 99.96%. Additionally, network throughput degrades by less than 10% when injecting three random link faults without disabling any node. In contrast, a mechanism similar to the one proposed in the BlueGene/L, that disables some network planes, would strongly degrade network throughput by 79%.