Anonymization-based privacy protection ensures that published data cannot be linked back to an individual. The most common approach in this domain is to apply generalizations on the private data in order to maintain a privacy standard such as k-anonymity. While generalization-based techniques preserve truthfulness, relatively small output space of such techniques often results in unacceptable utility loss especially when privacy requirements are strict. In this paper, we introduce the hybrid generalizations which are formed by not only generalizations but also the data relocation mechanism. Data relocation involves changing certain data cells to further populate small groups of tuples that are indistinguishable with each other. This allows us to create anonymizations of finer granularity confirming to the underlying privacy standards. Data relocation serves as a tradeoff between utility and truthfulness and we provide an input parameter to control this tradeoff. Experiments on real data show that allowing a relatively small number of relocations increases utility with respect to heuristic metrics and query answering accuracy.