The Gent-McWilliams (GM) and Redi eddy parameterizations are essential features to ocean climate models. GM helps to maintain stratification, balancing the steepening of isopycnals by Ekman forcing and convection with a relaxation that dissipates potential energy adiabatically. The Redi parametrization represents unresolved isopycnal mixing of tracers, while keeping diabatic mixing small. Due to its direct impact on the simulated circulation, research has focused more on theories for the GM than Redi coefficient, the latter typically being set equal to the former without justification. Theories for the GM coefficient invariably rely on an assumption of down-gradient eddy buoyancy fluxes, despite that estimates of the latter in eddy-resolving models and nature often show up-gradient tendencies. When tuned to values of O(500) $m^2s^{-1}$, GM-based simulations are able to reproduce observed ocean stratification. By contrast, observational estimates of along-isopycnal mesoscale diffusivity (the Redi part) are typically an order of magnitude larger. Setting the Redi coefficient to the too-small GM value results in serious errors in biogeochemical tracers like oxygen. Here I will describe an alternate approach that requires only small changes to the existing infrastructure and resolves the discrepancy in values. The idea relies on three results: (1) materially-conserved tracers are mixed down-gradient, with diffusivities well-estimated by mixing-length theory; (2) the mixing rate of tracers and potential vorticity (PV) are very similar; (3) eddy PV and buoyancy fluxes are related through an integral relationship derived from quasigeostrophic theory. Therefore, I argue that PV flux theories should be applied to setting the Redi coefficient, with the GM coefficient determined diagnostically. This idea is explored using a high-resolution MITgcm simulation of an idealized Southern Ocean channel, run with 10 independent tracers, each driven by different mean gradients. The tracers are used to extract an estimate of the mixing tensor, and hence of the mixing coefficients in question.