Contrail cirrus, formed in the wake of an aircraft, contributes significantly to aviation's climate impact. Diverting aircraft from ice-supersaturated regions (ISSRs) can mitigate this, as contrails can form and persist there. ISSRs can form when rising air cools to ice supersaturation; the same motion can cause clear air turbulence (CAT). This motivates characterising the turbulence risk associated with diversions to avoid ISSRs. Analysing the global log odds ratio distribution from ERA5 reanalysis data reveals a relationship between ISSRs and moderate-or-greater (MOG) CAT. However, the directionality of the relationship is highly sensitive to the three turbulence diagnostics used (i.e., Turbulence Index 1, NCSU1 and Brown 2). For contrail avoidance, a positive relationship presents an opportunity to mitigate both the climate impact and turbulence risk. Conversely, the opposite poses a potential trade-off between the two. Despite the sensitivity, there is agreement across the three turbulence diagnostics that: 1) when large-scale movements of air are encountered in the mid-latitudes, a pattern in the direction of the turbulence risk change emerges across the vertical velocity regimes; in particular, ISSRs in a strong updraft have on average a +19.0% increased risk of MOG CAT, and 2) in the mid-latitudes, the overall risk of MOG CAT in an ISSR is higher in winter (+33.3%, on average) and lower in summer (−42.6%). Collectively, these findings suggest that vertical velocity may differentiate two classes of ISSRs: those associated with an increased risk of MOG CAT and those that are not. This lays the groundwork to exploit this relationship to improve the operational efficiency of climate-optimised flight trajectories.