We introduce an easily implemented and flexible calibration technique for partial demand systems, combining recent developments in incomplete demand systems and a set of restrictions conditioned on the available elasticity estimates. The technique accommodates various degrees of knowledge on cross-price elasticities, satisfies curvature restrictions, and allows the recovery of an exact welfare measure for policy analysis. The technique is illustrated with a partial demand system for food consumption in Korea for different states of knowledge on cross-price effects. The consumer welfare impact of food and agricultural trade liberalization is measured.