We examine the question of whether Leontief's [15] conditions for separability and aggregation need be approximately satisfied if only approximate aggregates are to be constructed. It is found that they must be approximately satisfied unless the functions involved exhibit increasingly irregular behavior as the approximation involved in the aggregate gets better. The irregularities involved are related to the violation of Lipschitz Conditions. The stringency of the Leontief conditions for aggregation is therefore not easily evaded.