In this paper we propose a maximum likelihood technique to combat amplitude scaling attacks within a quantization-based watermarking context. We concentrate on operations that are common in many applications and at the same time devastating to this class of watermarking schemes, namely, amplitude scaling in combination with additive noise. First we derive the probability density function of the watermarked and attacked data in the absence of subtractive dither. Next we extend these models to incorporate subtractive dither in the encoder. The dither sequence is primarily used for security purposes, and the dither is assumed to be known also to the decoder. We design the dither signal statistics such that an attacker having no knowledge of the dither cannot decode the watermark. Using an approximation of the probability density function in the presence of subtractive dither, we derive a maximum likelihood procedure for estimating amplitude scaling factors. Experiments are performed with synthetic and real audio signals, showing the feasibility of the proposed approach under realistic conditions.