A method and system is provided for culling hidden objects in a tile-based graphics system before they are indicated in a display list for a tile. A rendering space is divided into a plurality of regions which may for example be a plurality of tiles or a plurality of areas into which one or more tiles are divided. Depth thresholds for the regions, which are used to identify hidden objects for culling, are updated when an object entirely covers a region and in dependence on a comparison between a depth value for the object and the depth threshold for the region. For example, if the depth threshold is a maximum depth threshold, the depth threshold may be updated if an object entirely covers the tile and the maximum depth value of the object is less than the maximum depth threshold.