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Simulations of the clustering of cold dark matter yield dark-matter halosthat have central density cusps, but observations of totally dark-matterdominated dwarf spheroidal galaxies imply that they do not have cuspy centraldensity profiles. We use analytic calculations and numerical modelling to arguethat whenever stars form, central density cusps are likely to be erased. Gasthat accumulates in the potential well of an initially cuspy dark-matter halosettles into a disc. Eventually the surface density of the gas exceeds thethreshold for fragmentation into self-gravitating clouds. The clouds aremassive enough to transfer energy to the dark-matter particles via dynamicalfriction on a short time-scale. The halo's central cusp is heated to form acore with central logarithmic density slope gamma=0 before stellar feedbackmakes its impact. Since star formation is an inefficient process, the cloudsare disrupted by feedback when only a small fraction of their mass has beenconverted to stars, and the dark matter dominates the final mass distribution.

Early flattening of dark matter cusps in dwarf spheroidal galaxies