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Payment transaction channels are one of the main proposed approaches to scaling cryptocurrency payment systems. Recent work by Malavolta et al. [7] has shown that the privacy of the protocol may conflict with its concurrent nature and may lead to deadlocks. In this paper we ask the natural question: can payments in routing networks be routed so as to avoid deadlocks altogether? Our results show that it is in general NP-complete to determine whether a deadlock-free routing exists in a given payment graph. On the other hand, Given some fixed routing, we propose another way to resolve the problem of deadlocks. We offer a modification of the protocols in lightning network and in Fulgor [7] that pre-locks edges in an order that guarantees progress, while still maintaining the protocol’s privacy requirements.