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This paper describes how to establish trust for P2P storage using a payment-based scheme. This scheme relies on the monitoring of storage peers on a regular basis. The verification operations allow assessing peer behavior and eventually estimating their subsequent remuneration or punishment. The periodic verification operations are used to enforce the fair exchange of a payment against effective cooperative peer behavior. Payments are periodically provided to peers based on the verification results. Only cooperative peers are paid by data owners with the help of intermediates in the P2P network, thus accommodating peer churn. Moreover, our payment scheme does not require any centralized trusted authority to appropriately realize a large-scale system. Simulations in this paper evaluate the capability of the payment scheme to work as a sieve to filter out non cooperative peers.