This paper derives a set of linear and nonlinear restrictions to make a n-goods linear AIDS symmetric when all prices are allowed to vary. When prices are scaled by their means, the conventional restrictions are sufficient to make the linear AIDS symmetric at mean. This indicates an additional advantage of scaling prices at their means before estimation. Nevertheless, price-scaling does not produce a globally-symmetric linear AIDS. When prices are measured in natural units, additional nonlinear restrictions are needed to make the linear AIDS globally symmetric. These restrictions can be imposed with relative ease but convert the linear AIDS into the nonlinear one. The significance of the problem was illustrated using both the US and Canada meat consumption data sets. In both cases, there is a marked difference between the nonlinear and linear AIDS. The bias in the implied values of demand elasticities is more serious in the US data set. Also the mean-symmetric linear AIDS does not improve much on the asymmetric and symmetric linear AIDS.