Commerce: Dealing with double-spending

The tricky bit of electronic cash is that coins are just bits, and so are easy to copy.  There are three approaches to this problem:
Smartcards
Store coins (or account balance) in tamper-resistant hardware (Mondex does this).
Online double-spending prevention
Require that the merchant contact the bank, and make sure the coins it was given have not yet been spent, before completing the transaction with the customer (Chaum's system does this).
Offline double-spending detection
Possibly in addition to using smartcards, identify cheaters after the fact (Brands' system does this).
You don't need to contact the bank in the middle of every transaction.
Arrange that the bank account number is completely hidden if you spend a coin once, but revealed if you spend it twice!