This paper deals with the use of the Koetter-Vardy soft-decision decoding algorithm to perform identification of guilty users in traitor tracing and fingerprinting schemes. In these schemes, each user is assigned a copy of an object with an embedded codeword. Placing different codewords in different copies makes each copy unique and at the same time allows unique identification of each user. The weakness of these schemes comes in the form of a collusion attack, where a group of dishonest users get together and, by comparing their copies, they create a pirate copy that tries to hide their identities. The concern of the paper is restricted to traitor tracing and fingerprinting schemes based on Reed-Solomon codes. By using the Koetter-Vardy soft-decision decoding algorithm as the core part of the tracing process, three different settings are approached: tracing in traceability codes, tracing in identifiable parent property codes and tracing in binary concatenated fingerprinting codes. It is also discussed how by a careful setting of a reliability matrix all possibly identifiable users can be found.