Collusion-secure codes are used for digital fingerprinting and for traitor tracing. In both cases, the goal is to prevent unauthorised copying of copyrighted material, by tracing at least one guilty user when illegal copies appear. The most well-known collusion-secure code is due to Boneh and Shaw (1995/98). In this paper we improve the decoding algorithm by using soft output from the inner decoder, and we show that this permits using significantly shorter codewords.