Stability and convergence of the modified EVP implementation of the visco-plastic sea ice rheology by Bouillon et al., Ocean Modell., 2013, is analyzed on B- and C-grids. It is shown that the implementation on a B-grid is less restrictive with respect to stability requirements than on a C-grid. On C-grids convergence is sensitive to the discretization of the viscosities. We suggest to adaptively vary the parameters of pseudotime subcycling of the modified EVP scheme in time and space to satisfy local stability constraints. This new approach generally improves the convergence of the modified EVP scheme and hence its numerical efficiency. The performance of the new “adaptive EVP” approach is illustrated in a series of experiments with the sea ice component of the MIT general circulation model (MITgcm) that is formulated on a C-grid