Micropayment schemes usually do not provide fairness, which means that either the payer or the payee, or both, can cheat the other and gain a financial advantage by misbehaving in the protocols. We propose an extension to a family of micropayment schemes that removes the financial incentive to cheat. Our extension does not provide true fairness, but it makes misbehaving practically futile for both the payer and the payee. We achieve this without any substantial loss in efficiency, in most practical cases.