Bright high harmonic sources can be produced by loosely focussing high peak power laser pulses to exploit the quadratic scaling of flux with driver spot size at the expense of a larger experimental footprint. Here, we present a method for increasing the brightness of a harmonic source (while maintaining a compact experimental geometry) by spatially shaping the transverse focal intensity distribution of a driving laser from a Gaussian to supergaussian. Using a phase-only spatial light modulator we increase the size and order of the supergaussian focal profiles, thereby increasing the number of harmonic emitters more efficiently than possible with Gaussian beams. This provides the benefits of a loose focussing geometry, yielding a five-fold increase in harmonic brightness, whilst maintaining a constant experimental footprint. This technique can readily be applied to existing high harmonic systems, opening new opportunities for applications requiring bright, compact sources of coherent short wavelength radiation.