Peaking the density profile increases the usable bootstrap current and the average fusion power density; this could reduce the current drive power and increase the net output of power producing tokamaks. The use of neutral beams and pellet injection to produce peaked density profiles is assessed. It is shown that with radially 'hollow' diffusivity profiles (and no particle pinch) moderately peaked density profiles can be produced by particle source profiles that are peaked off-axis. The fuelling penetration requirements can therefore be relaxed and this greatly improves the feasibility of generating peaked density profiles in large tokamaks. In particular, neutral beam fuelling does not require megavolt particle energies. Even with beam voltages of approximately 200 keV, however, exceptionally good particle confinement is needed to achieve net electrical power generation. The required ratio of particle to thermal diffusivities is an order of magnitude outside the range reported for tokamaks. In a system with no power production requirement (e.g., neutron sources) neutral beam fuelling should be capable of producing peaked density profiles in devices as large as ITER. Fuelling systems with low energy cost per particle-such as cryogenic pellet injection-must be used in power producing tokamaks when tau p approximately tau E. Simulations with pellet injection speeds of 7 km/s show that the peaking factor, ne0/(ne), approaches 2