Organometal halide perovskites exhibit large bulk crystal domain sizes, rare traps, excellent mobilities and carriers that are free at room temperature - properties that support their excellent performance in charge-separating devices. In devices that rely on the forward injection of electrons and holes, such as light-emitting diodes (LEDs), excellent mobilities contribute to the efficient capture of non-equilibrium charge carriers by rare non-radiative centres. Moreover, the lack of bound excitons weakens the competition of desired radiative (over undesired non-radiative) recombination. Here we report a perovskite mixed material comprising a series of differently quantum-size-tuned grains that funnels photoexcitations to the lowest-bandgap light-emitter in the mixture. The materials function as charge carrier concentrators, ensuring that radiative recombination successfully outcompetes trapping and hence non-radiative recombination. We use the new material to build devices that exhibit an external quantum efficiency (EQE) of 8.8% and a radiance of 80W sr-1m-2. These represent the brightest and most efficient solution-processed near-infrared LEDs to date.