Bond refunding is a zero-sum game against the market. Market efficiency implies that a callable bond is, ex ante, no more or less attractive than a noncallable bond. The decision maker can be presumed to have no superiority over bond investors in predicting future interest rates. Consideration of the refunding problem in the context of an efficient market allows the problem to be handled by a model involving a single refunding and a single state variable. In this way, a significant simplification of the formal structure of the problem is achieved without loss of generality. It is desirable in the refunding problem to establish conditions under which the current decision can be made without considering all possible future actions. A myopic refunding policy is defined as one based solely on comparison of the costs from refunding immediately with those from refunding in the next period. It is shown that a myopic policy is optimal when a condition is imposed on the distribution of future interest rates. This condition is consistent with a pattern of expectations that is of practical interest.