A utility tree is specified yielding a complete set of demand equations that subsumes the linear expenditure system as a special case. In contrast to the Stone-Geary system, it is shown that our S-branch model allows for Hicks-Allen complements, and it does not restrict the own-price elasticity. Moreover, it is not costly in terms of the additional parameters required. Maximum-likelihood estimates of the S-branch system are presented; these are derived by means of the Bard version of the Gauss-Newton algorithm. In this application to food expenditure data in the United States the use of the S-branch system avoids a potential misspecification which would have resulted from the application of the linear expenditure system.