A novel quantization-based data-hiding method, named Rational Dither Modulation (RDM), is presented. This method retains most of the easiness of the Dither Modulation (DM) scheme, which is known to be vulnerable to fixed-gain attacks. However, RDM modifies DM in such a way that it becomes invariant to those attacks. The basic principle behind RDM is the use of an adaptive quantization step-size at both embedder and decoder, which depends on previously watermarked samples. When the host signal is stationary, this causes the watermarked signal being under some mild conditions asymptotically stationary. Mathematical tools, new to data-hiding, are used to determine this stationary probability density function, which is later employed to analytically establish the performance of RDM in Gaussian channels. We also show that by properly increasing the memory of the system, it is possible to asymptotically approach the performance of conventional DM, while still keeping invariance to fixed gain attacks. Moreover, RDM is compared to improved spread-spectrum (ISS) methods, showing that for the former much higher rates can be achieved for the same bit error probability. Our theoretical results are validated with experimental results, which also serve to show a moderate resilience of RDM in front of slow-varying gain attacks. Perhaps the main advantage of RDM in comparison with other schemes designed to cope with fixed-gain attacks is its simplicity.