An important restriction which frequently appears in the bid specifications for new issues of municipal bonds is that the total dollar amount to be paid for both principal and interest by the municipality in any given year of the issue must not be significantly different from the total dollar amount to be paid in any other year, i.e., that the total payout pattern over the lifetime of the bond issue must be substantially level. Because of this “level debt” restriction, the inter-relationships between coupon schedule and maturity schedule appear to underwriters as being very complex. Given the requirements of the marketplace, bond market professionals presently employ trial-and-error techniques in an attempt to determine the admissible coupon and maturity schedule which will lead to the lowest possible net interest cost. The present paper shows that the determination of this optimal coupon and maturity schedule for a level debt issue can be readily accomplished by linear programming techniques.