In this paper, we present some major algorithmic improvements to fast correlation attacks. In previous articles about fast correlations, algorithmics never was the main topic. Instead, the authors of these articles were usually addressing theoretical issues in order to get better attacks. This viewpoint has produced a long sequence of increasingly successful attacks against stream ciphers, which share a main common point: the need to find and evaluate parity-checks for the underlying linear feedback shift register. In the present work, we deliberately take a different point of view and we focus on the search for efficient algorithms for finding and evaluating parity-checks. We show that the simple algorithmic techniques that are usually used to perform these steps can be replaced by algorithms with better asymptotic complexity using more advanced algorithmic techniques. In practice, these new algorithms yield large improvements on the efficiency of fast correlation attacks.