Our extremely deep survey for extragalactic HI (HIDEEP) finds no intergalactic gas clouds, and no galaxies with HI at inferred global column-densities below 10^20 cm^-2 when we could have detected such objects down to a completeness limit of 4 x 10^18 cm^-2. We speculate that low surface-density hydrogen is either ionised or locked up in ``frozen discs, i.e. structures where the local Ly-alpha is insufficient to excite the 21-cm transition to a spin-temperature above the cosmic background. Such ``frozen discs might be responsible for many QSOALSs.