Nanopores that approach molecular dimensions demonstrate exotic transport behaviour and are theoretically predicted to display discontinuities in the diameter dependence of interior ion transport because of structuring of the internal fluid. No experimental study has been able to probe this diameter dependence in the 0.5-2 nm diameter regime. Here we observe a surprising fivefold enhancement of stochastic ion transport rates for single-walled carbon nanotube centered at a diameter of approximately 1.6 nm. An electrochemical transport model informed from literature simulations is used to understand the phenomenon. We also observe rates that scale with cation type as Li(+)>K(+)>Cs(+)>Na(+) and pore blocking extent as K(+)>Cs(+)>Na(+)>Li(+) potentially reflecting changes in hydration shell size. Across several ion types, the pore-blocking current and inverse dwell time are shown to scale linearly at low electric field. This work opens up new avenues in the study of transport effects at the nanoscale.