Nowadays, a popular method used for additive watermarking is wide spread spectrum. It consists in adding a spread signal into the host document. This signal is obtained by the sum of a set of carrier vectors, which are modulated by the bits to be embedded. To extract these embedded bits, weighted correlations between the watermarked document and the carriers are computed. Unfortunately, even without any attack, the obtained set of bits can be corrupted due to the interference with the host signal (host interference) and also due to the interference with the others carriers (inter-symbols interference (ISI) due to the non-orthogonality of the carriers). Some recent watermarking algorithms deal with host interference using side informed methods, but inter-symbols interference problem is still open. In this paper, we deal with interference cancellation methods, and we propose to consider ISI as side information and to integrate it into the host signal. This leads to a great improvement of extraction performance in term of signal-to-noise ratio and/or watermark robustness.