Personalization systems exploit preferences for providing users with only relevant data from the huge volume of information that is currently available. We consider preferences that dependent on context, such as the location of the user. We model context as a set of attributes, each taking values from hierarchical domains. Often, the context of the query may be too specific to match any of the given preferences. In this paper, we consider possible expansions of the query context produced by relaxing one or more of its context attributes. A hierarchical attribute may be relaxed upwards by replacing its value by a more general one, downwards by replacing its value by a set of more specific values or sideways by replacing its value by sibling values in the hierarchy. We present an algorithm based on a prefix-based representation of context for identifying the preferences whose context matches the relaxed context of the query and some initial performance results.