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Laser brightness is a measure of the ability to de- liver intense light to a target, and encapsulates both the energy content and the beam quality. High brightness lasers requires that both parameters be maximised, yet standard laser cavities do not allow this. For example, in solid-state lasers multimode beams have a high energy content but low beam quality, while Gaussian modes have a small mode volume and hence low energy extraction, but in a good quality mode. Here we over- come this fundamental limitation and demonstrate an optimal approach to realising high brightness lasers. We employ intra- cavity beam shaping to produce a Gaussian mode that carries all the energy of the multimode beam, thus energy extraction and beam quality are simultaneously maximised. This work will have a significant influence on the design of future high brightness laser cavities.