During the growth of Drosophila imaginal discs a process called 'cell competition' eliminates slow-proliferating but otherwise viable cells. We report here that cell competition requires the function of the brinker (brk) gene, whose expression is normally repressed by Decapentaplegic (Dpp) signalling but is upregulated in slow-growing Minute/+ cells. Excess brk expression activates the c-Jun amino-terminal kinase pathway, which in turn triggers apoptosis in these cells. We propose that slow-proliferating cells upregulate Brk levels owing to a disadvantage in competing for, or in transducing, the Dpp survival signal. This sequence of events might represent a general mechanism by which weaker cells are eliminated from a growing population, and might serve as a method of controlling cell number and optimizing tissue fitness and hence organ function.