Existing bilateral trade agreements often carry the restriction that hard currency or gold must be used to settle trade balances that have exceeded specified margins of credit. By means of a scheme of mutual cancellation of balances among several countries, it is hoped to get a larger volume of trade within the framework of a system of bilateral agreements containing such restrictive provisions. The simple mathematics of a compensation scheme of M. H. Ekker is presented. The main principle is the minimization, in the square, of the sum of balances under realistic types of constraints.