Abstract Vertical exchange of heat and carbon in the ocean regulates Earth’s climate. Convection, a driver of near surface exchange, occurs when dense water overlies light water. Fofonoff (1957) pointed out that when lighter overlying cold-fresh water mixes with denser underlying warm-salty water, the mixture can become denser than the underlying water due to a nonlinear process known as cabbeling. He suggested that such profiles, despite being gravitationally stable, could be classed as being unstable to cabbeling. Fofonoff (1957) hypothesised that, by mixing away such profiles, cabbeling may be shaping the thermohaline structure of polar oceans. We investigate this hypothesis here. In a one-dimensional model we find that convective mixing occurs in temperature inverted profiles that are unstable to cabbeling even when they are initially gravitationally stable. In data from an observationally constrained global circulation model, we find profiles with a temperature inversion larger than −0.5°C are unstable to cabbeling less than 0.02% of the time and in high quality in-situ observations they are unstable less than 12% of the time. We find that due to cabbeling larger temperature inversions, which should weaken stratification, make profiles more stable. Our results suggest that cabbeling limits the stability behaviour of temperature inverted profiles and influences the thermohaline structure in parts of the ocean where cold-fresh water overlays warm-salty water.