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A novel quantization-based data-hiding method, called Rational Dither Modulation (RDM), is presented. This method retains most of the simplicity of the conventional dither modulation (DM) scheme, which is largely vulnerable to amplitude scalings and modifies it in such a way that the result becomes invariant to gain attacks. RDM is based on using a gain-invariant adaptive quantization step-size at both embedder and decoder. This causes the watermarked signal to be asymptotically stationary. Mathematical tools are used to determine the stationary probability density function, which is later used to assess the performance of RDM in Gaussian channels. It is also shown that by increasing the memory of the system, it is possible to asymptotically approach the performance of DM, still keeping invariance against gain attacks. RDM is compared with improved spread-spectrum methods, showing that the former can achieve much higher rates for the same bit error probability. Experimental results confirm the validity of the theoretical analyses given in the paper. Finally, a broader class of methods, that extends gain-invariance to quantization index modulation (QIM) methods, is also presented.