Current off-line electronic cash systems require a great number of complex online computations by clients during the payment phase. In this paper, we propose a new off-line anonymous cash scheme that greatly reduces the number of online computations that need to be done by the clients for each payment transaction. In particular, except for the first coin in a transaction, the client only needs to perform minimal computations for the remaining coins in the transaction. Our scheme also provides unconditional client anonymity and is able to detect double-spending and is resistant to coin forgery and framing attacks.