Cross-sectional data are used to estimate a three-equation generalised addilog demand system (GADS); two equations are used to express the demand for milk by method of sale and a residual equation is used to close the system. It is shown that, as the average budget share of the residual equation approaches unity, the GADS equations for the incomplete system are approximately equivalent to double logarithmic equations. It is found that aggregate milk demand is relatively insensitive to both price and income, but the degree of substitution between delivered and non-delivered milk is both large and highly significant. A new test for influential data in the system context is developed and it suggests that the reported results are robust to variations in the sample space.