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Differential Privacy (DP) formalizes privacy in mathematical terms and provides a robust concept for privacy protection. DIfferentially Private Data Synthesis (DIPS) techniques produce and release synthetic individual-level data in the DP framework. One key challenge to develop DIPS methods is the preservation of the statistical utility of synthetic data, especially in high-dimensional settings. We propose a new DIPS approach, STatistical Election to Partition Sequentially (STEPS) that partitions data by attributes according to their importance ranks according to either a practical or statistical importance measure. STEPS aims to achieve better original information preservation for the attributes with higher importance ranks and produce thus more useful synthetic data overall. We present an algorithm to implement the STEPS procedure and employ the privacy budget composability to ensure the overall privacy cost is controlled at the pre-specified value. We apply the STEPS procedure to both simulated data and the 2000–2012 Current Population Survey youth voter data. The results suggest STEPS can better preserve the population-level information and the original information for some analyses compared to PrivBayes, a modified Uniform histogram approach, and the flat Laplace sanitizer.