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Abstract Using high-resolution data from Solar Orbiter, we investigate the plasma conditions necessary for the proton temperature-anisotropy-driven mirror-mode and oblique firehose instabilities to occur in the solar wind. We find that the unstable plasma exhibits dependencies on the angle between the direction of the magnetic field and the bulk solar wind velocity which cannot be explained by the double-adiabatic expansion of the solar wind alone. The angle dependencies suggest that perpendicular heating in Alfvénic wind may be responsible. We quantify the occurrence rate of the two instabilities as a function of the length of unstable intervals as they are convected over the spacecraft. This analysis indicates that mirror-mode and oblique firehose instabilities require a spatial interval of length greater than 2–3 unstable wavelengths in order to relax the plasma into a marginally stable state and thus closer to thermodynamic equilibrium in the solar wind. Our analysis suggests that the conditions for these instabilities to act effectively vary locally on scales much shorter than the correlation length of solar wind turbulence.