Efficiency of optimistic fair exchange using trusted devices is studied. Pfitzmann, Schunter and Waidner (PODC 1998) have shown that four messages in the main sub-protocol is optimal when exchanging idempotent items using non-trusted devices. It is straightforward that when using trusted devices for exchanging nonidempotent items this number can be reduced to three. This however comes at the cost of providing trusted devices with an unlimited amount of storage. We prove that exchanging non-idempotent items using trusted devices with a limited storage capacity requires exactly four messages in the main sub-protocol.