Recovery of traffic in connectionless pure IP networks has traditionally been handled by a full re-convergence of the network state. This process operates in a time scale that is not compatible with new real time and highly dependable services. Recently, schemes for fast local and proactive recovery in connectionless IP networks have been proposed. All these schemes are designed to guarantee recovery of the failure of one component. As IP protocols are used to carry more highly dependable services and new wireless infrastructures are approaching, guaranteed failure coverage of more than one failure becomes necessary. In this paper we present and evaluate a scheme that guarantees to handle any two concurrent failures in a network. We are not aware of any other schemes that addresses such guarantees. We evaluate and compare it with other known recovery schemes, and we show how it gives substantially better recovery success rates than the schemes designed for one fault tolerance, also for more than two failures.