Extreme electron accumulation with sheet density greater than 1013??cm-2 is almost universally present at the surface of indium nitride (InN). Here, x-ray photoemission spectroscopy and secondary ion mass spectrometry are used to show that the surface Fermi level decreases as the Mg concentration increases, with the sheet electron density falling to below 108??cm-2. Surface space-charge calculations indicate that the lowering of the surface Fermi level increases the density of unoccupied donor-type surface states and that these are largely compensated by Mg acceptors in the near-surface hole depletion region rather than by accumulated electrons. This is a significant step towards the realization of InN-based optoelectronic devices.