We have earned out an extremely long integration time (9000 s beam - 1 ) 21-cm blind survey of 60 deg 2 in Centaurus using the Parkes multibeam system. We find that the noise continues to fall as √t o b s throughout, enabling us to reach an HI column-density limit of 4.2 x 10 1 8 cm - 2 for galaxies with a velocity width of 200 km s - 1 in the central 32 deg 2 region, making this the deepest survey to date in terms of column density sensitivity. The H i data are complemented by very deep optical observations from digital stacking of multi-exposure UK Schmidt Telescope R-band films, which reach an isophotal level of 26.5 R mag arcsec - 2 (≃27.5 B mag arcsec - 2 ). 173 Hi sources have been found, 96 of which have been uniquely identified with optical counterparts in the overlap area. There is not a single source without an optical counterpart. Although we have not measured the column densities directly, we have inferred them from the optical sizes of their counterparts. All appear to have a column density of N H 1 = 10 2 0 . 6 5 ′ 0 . 3 8 . This is at least an order of magnitude above our sensitivity limit, with a scatter only marginally larger than the errors on N H 1 . This needs explaining. If confirmed it means that H 1 surveys will only find low surface brightness (LSB) galaxies with high M H 1 /L B . Gas-rich LSB galaxies with lower HI mass to light ratios do not exist. The paucity of low column-density galaxies also implies that no significant population will be missed by the all-sky H 1 surveys being carried out at Parkes and Jodrell Bank.