Privacy is an important concern in the society, and it has been a fundamental issue when to analyze and publish data involving human individual's sensitive information. Recently, the slicing method has been popularly used for privacy preservation in data publishing, because of its potential for preserving more data utility than others such as the generalization and bucketization approaches. However, in this paper, we show that the slicing method has disclosure risks for some absolute facts, which would help the adversary to find invalid records in the sliced microdata table, resulting in breach of individual privacy. To increase the privacy of published data in the sliced tables, a new method called value swapping is proposed in this work, aimed at decreasing the attribute disclosure risk for the absolute facts and ensuring the l‐diverse slicing. By value swapping, the published table contains no invalid information such that the adversary cannot breach the individual privacy. Experimental results also show that the NEW method is able to keep more data utility than the existing slicing methods in a published microdata table. Copyright © 2016 John Wiley & Sons, Ltd.