Recombined fingerprints have been suggested as a convenient approach to improve the efficiency of anonymous fingerprinting for the legal distribution of copyrighted multimedia contents in P2P systems. The recombination idea is inspired by the principles of mating, recombination and heredity of the DNA sequences of living beings, but applied to binary sequences, like in genetic algorithms. However, the existing recombination-based fingerprinting systems do not provide a convenient solution for collusion resistance, since they require double-layer fingerprinting codes, making the practical implementation of such systems a challenging task. In fact, collusion resistance is regarded as the most relevant requirement of a fingerprinting scheme, and the lack of any acceptable solution to this problem would possibly deter content merchants from deploying any practical implementation of the recombination approach. In this paper, this drawback is overcome by introducing two non-trivial improvements, paving the way for a future real-life application of recombination-based systems. First, Nuida et al.'s collusion-resistant codes are used in segment-wise fashion for the first time. Second, a novel version of the traitor-tracing algorithm is proposed in the encrypted domain, also for the first time, making it possible to provide the buyers with security against framing. In addition, the proposed method avoids the use of public-key cryptography for the multimedia content and expensive cryptographic protocols, leading to excellent performance in terms of both computational and communication burdens. The paper also analyzes the security and privacy properties of the proposed system both formally and informally, whereas the collusion resistance and the performance of the method are shown by means of experiments and simulations.