A model of a complete system of k linear expenditure functions introduced by Leser in 1960 [6, 7] has the advantage of great computational simplicity. An arbitrary specification, however, equating all cross elasticities of substitution results in unreliable estimate of price effects. In the present paper, a result in the theory of additive preferences [Houthakker, 5] is used in order to obtain a more plausible specification. This is achieved at the expense of an iterative procedure; however, the number of parameters (2k + 1) is identical in both models. A system of ten equations is fitted to Australian personal consumption data for the period 1949-50 to 1961-62.