Culling wildlife to control disease can lead to both decreases and increases in disease levels, with apparently conflicting responses observed, even for the same wildlife-disease system. There is therefore a pressing need to understand how culling design and implementation influence culling's potential to achieve disease control. We address this gap in understanding using a spatial metapopulation model representing wildlife living in distinct groups with density-dependent dispersal and framed on the badger- bovine tuberculosis (bTB) system. We show that if population reduction is too low, or too few groups are targeted, a 'perturbation effect' is observed, whereby culling leads to increased movement and disease spread. We also demonstrate the importance of culling across appropriate time scales, with otherwise successful control strategies leading to increased disease if they are not implemented for long enough. These results potentially explain a number of observations of the dynamics of both successful and unsuccessful attempts to control TB in badgers including the Randomized Badger Culling Trial in the UK, and we highlight their policy implications. Additionally, for parametrizations reflecting a broad range of wildlife-disease systems, we characterize 'Goldilocks zones', where, for a restricted combination of culling intensity, coverage and duration, the disease can be reduced without driving hosts to extinction.