Scaling attacks are well-known to be some of the most harmful strategies against quantization-based watermarking methods, as they desynchronize the decoder, completely ruining the performance of the watermarking system with almost non perceptually altering the watermarked signal. In this paper we propose a new family of quantization-based methods, based on both Dither Modulation and Spread Transform Dither Modulation, oriented to deal with those attacks, and which presents another outstanding property: they produce perceptually shaped watermarks.