Nanolasers hold promise for applications including integrated photonics, on-chip optical interconnects and optical sensing. Key to the realization of current cavity designs is the use of nanomaterials combining high gain with high radiative efficiency. Until now, efforts to enhance the performance of semiconductor nanomaterials have focused on reducing the rate of non-radiative recombination through improvements to material quality and complex passivation schemes. Here we employ controlled impurity doping to increase the rate of radiative recombination. This unique approach enables us to improve the radiative efficiency of unpassivated GaAs nanowires by a factor of several hundred times while also increasing differential gain and reducing the transparency carrier density. In this way, we demonstrate lasing from a nanomaterial that combines high radiative efficiency with a picosecond carrier lifetime ready for high speed applications.