Dwarf spheroidal galaxies have shallow central dark matter density profiles, low angular momentum and approximately exponential surface brightness distributions. Through N-body simulations and analytic calculations we investigate the extent to which these properties can be generated from ‘typical’ΛCDM galaxies, which differ in all of these properties, by the dynamical consequences of feedback. We find that, for a wide range of initial conditions, one impulsive mass-loss event will naturally produce a surface brightness profile in the remaining stellar component of a dwarf spheroidal galaxy (dSph) which is well-fitted over many scalelengths by an exponential, in good qualitative agreement with observations of Local Group dSphs. Furthermore, two impulsive mass-loss phases, punctuated by significant gas re-accretion, are found to be sufficient to transform a central density cusp in the dark matter profile into a near-constant density core. This may then provide the missing link between current cosmological simulations, which predict a central cusp in the dark matter density profile, and current observations, which find much shallower central density profiles. We also look at the angular momentum history of dSphs and demonstrate that if these galaxies have spent most of their lifetime in tidal isolation from massive galaxies then they cannot have formed from high angular momentum gas discs.