We are grateful to Carmen Beviá, Howard Petith, an associate editor, and two anonymous referees for their very helpful comments and suggestions. Financial support through a grant from the Programa de Cooperación Cientifica Iberoamericana is acknowledged. The work of Jordi Massó is also partially supported by Research Grants PB98-0870 from the Dirección General de Investigación Cientı́fica y Técnica, Spanish Ministry of Education, and SGR98-62 from the Comissionat per Universitats i Recerca de la Generalitat de Catalunya. The paper was partially written while Alejandro Neme was visiting the Universitat Autònoma de Barcelona under a sabbatical fellowship from the Generalitat de Catalunya

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, then the uniform allocation rule is the unique strategy-proof, efficient, and anonymous rule. We identify the maximal set of preferences, containing the set of single-peaked preferences, under which there exists at least one rule satisfying the properties of strategy-proofness, efficiency, and strong symmetry. In addition, we show that our characterization implies a slightly weaker version of Ching and Serizawa's (1998) result. Journal of Economic Literature Classification Numbers: D71, D78, D63.