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Look-up table (LUT)-based data hiding is a simple and efficient technique to hide secondary information (watermark) into multimedia work for various applications such as copyright protection, transaction tracking or content annotation. This paper studies the distortion introduced by a general LUT-based data hiding. We find that designing LUT according to the distribution of host data and watermark data can greatly reduce the distortion of LUT embedding. A new practical reduced-distortion LUT design method is developed for robust data hiding. The new method is applied in a wavelet domain image data hiding system and only significant wavelet coefficients are used to embed the watermark. A Gaussian mixture model and a related expectation-maximization algorithm-based method are employed to model the statistical distribution of the host image. The statistical model is used to select significant coefficients of the host image for data hiding. The experimental results show that compared to the conventional odd-even LUT embedding method, the presented new LUT data hiding algorithm provides average 1. 5-2. 5 dB PSNR improvement and better robustness for image watermarking.