Digital watermarks emerged in the last decade as a possible solution for protecting the copyright of digital materials. We introduce complex wavelets as a novel transform for watermarking images. The complex wavelets transform has similar properties to the human visual system and experimental results show that watermarking systems designed using complex wavelets have good performance. Two different watermarking systems are considered here. The first one is based on the principles of spread spectrum communications. An alternative matched filter is proposed for watermark decoding, which is shown to have better performance than the conventional matched filter, when the underlying signal is non-stationary. The second watermarking algorithm is based on a hybrid combination between quantisation and spread spectrum techniques. This is due to the fact that watermarking can be considered as communication with side information. Finally, we suggest ways in which the watermark decoder performance can be improved when the watermarked image is attacked, in particular under three scenarios: compression, geometric distortion and denoising.