The cattle tracing databases set up over the past decades in Europe have become major resources for representing demographic processes of livestock and assessing potential risk of infections spreading by trade. The herds registered in these databases are nodes of a network of commercial movements, which can be altered to lower the risk of disease transmission. In this study, we develop an algorithm aimed at reducing the number of infected animals and herds, by rewiring specific movements responsible for trade flows from high- to low-prevalence herds. The algorithm is coupled with a generic computational model describing infection spread within and between herds, based on data extracted from the French cattle movement tracing database (BDNI). This model is used to simulate a wide array of infections, with either a recent outbreak (epidemic) or an outbreak that occurred five years earlier (endemic), on which the performances of the rewiring algorithm are explored. Results highlight the effectiveness of rewiring in containing infections to a limited number of herds for all scenarios, but especially if the outbreak is recent and if the estimation of disease prevalence is frequent. Further analysis reveal that the key parameters of the algorithm affecting infection outcome vary with the infection parameters. Allowing any animal movement from high to low-prevalence herds reduces the effectiveness of the algorithm in epidemic settings, while frequent and fine-grained prevalence assessments improve the impact of the algorithm in endemic settings. According to our results, our approach focusing on a few commercial movements is expected to lead to substantial improvements in the control of a targeted disease, although changes in the network structure should be monitored for potential vulnerabilities to other diseases. Due to its generality, the developed rewiring algorithm could be applied to any network of controlled individual movements liable to spread disease