Abstract: Compared with existing payment systems, Bitcoin’s throughput is low. Designed to address Bitcoin’s scalability challenge, the Lightning Network is a protocol allowing two parties to secure bitcoin payments and escrow holdings between them. Payment-channel networks such as the Lightning Network enable off-chain payments secured by the channels’ balances as alternatives to on-chain transactions. This paper solves the optimal channel management problem for two agents who pay each other arbitrarily distributed amounts. Agents optimally choose the channel’s size and whether to make each payment on-chain or on-channel, depending on their current balance. This work, in collaboration with Paolo Guasoni, characterizes optimal channels and payment policies, describing an algorithm to obtain them, given payments’ frequency and distribution.