Several K-anonymity techniques, such as generalization and bucketization, have been designed for privacy preserving microdata publishing. Recent work has shown that generalization loses considerable amount of information, especially for high dimensional data. Bucketization, on the other hand, does not prevent membership disclosure and does not apply for data that do not have a clear separation between quasi-identifying attributes and sensitive attributes. In this paper, we present a novel technique called overlapping Slicing Techniques, which partitions the data both horizontally and vertically. We show that overlapping Slicing Techniques preserves better data utility than generalization and can be used for membership disclosure protection. Another important advantage of overlapping Slicing Techniques is that it can handle high-dimensional data storage.