What are the benefits provided by a payment system? What are the trade-offs in public versus private payment systems and in restricted versus open payments arrangements? Modern payment systems encompass a variety of institutional designs with varying degrees of counterparty protection. We develop a framework that allows for an examination and comparison of payment systems, and specification of conditions leading to their adoption. We relate these conditions to the design of present large-value payment systems (Fedwire, CHIPS, TARGET, etc.).