Some species cause significant harm owing to their ability to transmit disease, inflict damage and cause unwanted changes to the environment. Although a range of population control strategies exist, significant burden remains, and novel approaches are sorely needed. Genetic population control is a fast-developing field which involves releasing genetically modified organisms to reduce the reproductive capacity of wild populations. Of particular interest are synthetic gene drive constructs which offer efficient control owing to their ability to increase in frequency from rare and spread to neighbouring populations via migration. However, sometimes only local populations need control, and impact outside of the release area would be undesirable. In this study we aimed to identify and evaluate novel efficient and localisable strategies for population suppression and develop a systematic approach to strategy discovery. Using mathematical models, we explored a range of two-construct strategies which exploit differentiated sequences in the genome to prevent spread, finding that they offer highly efficient localisable suppression. We also developed a flexible simulator capable of modelling strategies built from combinations of different molecular components and genes. With this, we screened hundreds of thousands of possible strategies and identified a range of self-limiting designs whilst also revealing general principles which govern their persistence and suppression potential. We also identified a novel category of threshold- dependent self-sustaining drives, which offer high levels of localised suppression with achievable release thresholds. Finally, we performed an in-depth analysis of a category of self- limiting strategies found to offer efficient suppression when released under a repeat-release regime and explored various augmentations which improve efficiency. Overall, this work revealed a range of novel strategies for achieving efficient, yet localisable population control; produced a highly flexible simulator; and validated a new approach for strategy discovery, which combines theoretical understanding and computational power to uncover previously unknown control strategies.