A novel class of multigrid algorithms for the variable-coupling isotropic Gaussian models is presented. In addition to the elimination of the critical slowing down (which otherwise might become much worse than usual in the case of strongly varying coupling values), the “volume factor” is also eliminated. That is, the need to produce many independent fine-grid configurations for averaging out their statistical deviations is removed, by applying multigrid cycles that sample mostly on coarse grids. Thermodynamic limits can be calculated to relative accuracy ε r in just $$O(\varepsilon _r^{ - 2} )$$ computer operations, where ε r is the error relative to the standard deviation of the observable. In this paper, such an optimal algorithm is obtained for the calculation of the susceptibility in the d-dimensional variable-coupling isotropic Gaussian model (with numerical experiments for d = 1, 2). Some basic general rules for the operation of multigrid algorithms, applicable to much wider classes of models, are derived.