A recognized deficiency of ocean models with a constant-depth vertical coordinate is for truncation errors in the advection scheme to result in spurious numerical mixing of tracers, which can be substantial larger than that prescribed by the model’s mixing scheme. The z~ vertical coordinate allows vertical levels to displace in a lagrangian fashion on time scales shorter than a few days, but reverts to fixed levels on longer timescales, and is intended to reduce numerical mixing from transient vertical motions such as internal waves and tides. An assessment of z~ in a ¼° global implementation of the NEMO model is presented. It is shown that, in the presence of near-inertial gravity waves in the North Atlantic, z~ significantly reduces eulerian vertical velocities with respect to those in a control simulation with the default z* vertical coordinate; that the vertical coordinate approaches an isopycnal, or adiabatic, surface on short timescales; and that both tendences are enhanced when the z~ timescale parameters are lengthened with respect to the default settings. Evaluation of an effective diapycnal diffusivity, based on density transformation rates, shows that numerical mixing is consistently reduced as the z~ timescales are lengthened. The realism of the model simulation with different timescale parameters is assessed in the global domain, and it is shown that drifts in temperature and salinity, and the spindown in z*of the Antarctic Circumpolar Current, are reduced with z~, without incurring significant penalties in other metrics such as the strength of the overturning circulation or sea ice cover.