Mesoscale eddies are unresolved in most of today’s global ocean models, and their effect on the large-scale ocean circulation needs to be parameterized. Greatbatch and Lamb (1990, GL90) suggested an eddy form stress parameterization that mixes geostrophic momentum in the vertical. The GL90 vertical viscosity scheme, which is equivalent to the Gent and McWilliams (1990, GM90) parameterization under the geostrophic assumption, has seen only very limited use, and exclusively in models that use z-coordinates and are of very coarse resolution. In this paper, we explore the GL90 parameterization in an idealized isopycnal coordinate model, both from a theoretical and practical perspective. We further compare the effects of the GM90 and GL90 parameterizations across a range of non-eddying to eddy-permitting resolutions. From a theoretical perspective, the GL90 parameterization is more attractive than the GM90 scheme for isopycnal coordinate models because GL90 provides an interpretation that is fully consistent with thickness-weighted isopycnal averaging, while GM90 cannot be entirely reconciled with any fully isopycnal averaging framework. From a practical perspective, the GL90 and GM90 parameterizations lead to extremely similar energy levels, flow and vertical structure, even though their energetic pathways are very different. The equivalence holds true from non-eddying through eddy-permitting resolution. We conclude that in isopycnal coordinate models, the GL90 parameterization provides a good–if not equivalent–alternative to the GM90 parameterization. The GL90 parameterization is more advantageous in terms of computational efficiency, ease of implementation, and numerical stability.