This paper addresses the problem of threshold traitor tracing for digital content where, by embedding appropriate digital patterns into the distributed content, it is possible to trace and identify the source of unauthorised redistribution. We use a set of marking assumptions where the adversaries have varying powers to change or erase coordinates of the fingerprint where their individual fingerprints differ–and consider the implications. We propose new codes derived from combinatorial designs–and develop a method for concatenating these codes to filter out the false positives and defend against some of the attacks considered.