People's preferences are expressed at varying levels of granularity and detail as a result of partial or imperfect knowledge. One may have some preference for a general class of entities, e.g., liking comedies, and another one for a ne-grained, specic class, e.g., disliking recent thrillers with Al Pacino that are intended for families. In this paper, we are interested in capturing such complex, multi-granular preferences to personalize database queries and in studying their impact on query results. In particular, we organize the collection of one's preferences in a preference network (a directed acyclic graph), where each node refers to a subclass of the entities that its parent refers to, and whenever they both apply, more specic preferences override more generic ones. We study query personalization based on networks of preferences and provide ecient algorithms for identifying relevant preferences, modifying queries accordingly, and processing these queries to obtain personalized answers. Finally, we present results of both synthetic and realuser experiments, which (a) demonstrate the eciency of our algorithms, (b) provide insight as to the appropriateness of the proposed preference model and (c) show the benets of query personalization based on composite preferences compared to simpler preference representations.