Method determining lookup table ("LUT") for embedding watermark. For each quantization cell, calculating probabilities that signal point falls into cell. Selecting cell by probabilities. Setting LUT value to watermark value with largest probability, subject to run constraint. For remaining cells, repeating selecting and setting steps. Other method determining quantization ensemble by calculating probability density function for signal points where the watermark value to be embedded. Distortion and robustness functions are formulated. Given robustness or distortion is selected. Functions optimized, and ensemble of quantizers determined with parameters that comply. Other method quantizing in association with lossy compression. Strength of compression determined. Adapting strength of watermark with strength of compression by a mapping. Other method selecting points for embedding watermark. Determine threshold between large and small signal points using statistical method. Select signal points for embedding according to threshold. Also, processors, computer programs, and systems.