In this paper we answer a question posed by Sertel and Sanver (2002) on the manipulability of optimal matching rules in matching problems with endowments. We characterize the classes of consumption rules under which optimal matching rules can be manipulated via predonation of endowment.G. Fiestras-Janeiro received financial support from the Spanish Ministerio de Ciencia y Tecnología and the FEDER through projects PB98-0613-C02-02 and BEC2002-04102-C02-02, and from the Xunta de Galicia through grant PGIDT00PXI20703PN. The work of F. Klijn is partially supported by Research Grant BEC2002-02130 from the Spanish Ministerio de Ciencia y Tecnología and by a Marie Curie Fellowship of the European Community programme “Improving Human Research Potential and the Socioeconomic Knowledge Base” under contract number HPMF-CT-2001-01232. The work of E. Sánchez is supported by project BEC2002-04102-C02-02 from the Spanish Ministerio de Ciencia y Tecnología and the FEDER.