The natural H-mode density, i.e. the plasma density evolving in an H-mode discharge without active fuelling, reaches Greenwald fractions in JET typically higher than in ASDEX Upgrade. According to general thinking this re ects device-specic dierences as regards recycling induced fuelling and beam fuelling. This paper presents evidence for a dierent view, namely that at suciently low plasma fuelling rates any fuelling rate dependence of the plasma density vanishes and the plasma particle content is completely determined by the plasma itself. It is shown that this limit, which would constitute an additional H-mode operational boundary, is reached in JET and ASDEX Upgrade natural density discharges and its scaling is determined. Possible overlapping with existing density limit scalings in next generation tokamaks is discussed with a view to the potential implications for the H-mode operation window.