Detailed mechanistic modelling has been performed of the intercellular signalling cascade between precancerous cells and their normal neighbours that leads to a selective removal of the precancerous cells by apoptosis. Two interconnected signalling pathways that were identified experimentally have been modelled, explicitly accounting for temporal and spatial effects. The model predicts highly non-linear behaviour of the signalling. Importantly, under certain conditions, enhanced release of primary signals by precancerous cells renders the signalling ineffective. This counter-intuitive behaviour arises due to spatial aspects of the underlying signalling scheme: Increased primary signalling by precancerous cells does, upon reaction with factors derived from normal cells, produce higher yields of apoptosis-triggering molecules. However, the apoptosis-triggering signals are formed farther from the precancerous cells, so that these are attacked less efficiently. Spatial effects thus may represent a novel analogue of negative feedback mechanisms.