The concept of a semiflexible functional form is applied to the Almost Ideal (AI) demand system. This yields a demand model that is more parsimonious than standard ones while preserving a degree of flexibility, that satisfies the curvature property of concavity of the underlying expenditure function (at least locally), and that preserves the desirable properties of the AI model (aggregation across consumers and nonlinearity of the Engel curves). The model is illustrated with an application to a relatively large demand system emphasizing food consumption.