The many recent publications that focus upon watermarking with side information at the embedder emphasize the fact that this side information can be used to improve practical capacity. Many of the proposed algorithms use quantization to carry out the embedding process. Although both powerful and simple, recovering the original quantization levels, and hence the embedded data, can be difficult if the image amplitude is modified. In our paper, we present a method that is similar to the existing class of quantization-based techniques, but is different in the sense that we first apply a projection to the image data that is invariant to a class of amplitude modifications that can be described as order preserving. Watermark reading and embedding is done with respect to the projected data rather than the original. Not surprisingly, by requiring invariance to amplitude modifications we increase our vulnerability to other types of distortions. Uniform quantization of the projected data generally leads to non-uniform quantization of the original data, which in turn can cause greater susceptibility to additive noise. Later in the paper we describe a strategy that results in an effective compromise between invariance to amplitude modification and noise susceptibility.