The vast majority of ice-sheet modelling studies rely on simplified representations of the glacial isostatic adjustment (GIA), which, among other limitations, do not account for lateral variations in the lithospheric thickness and upper-mantle viscosity. In studies of the last glacial cycle using 3D GIA models, this has however been shown to have major impacts on the dynamics of marine-based sectors of Antarctica, which are likely to be the greatest contributors to sea-level rise in the coming centuries. This gap in comprehensiveness is explained by the fact that 3D GIA models are computationally expensive, rarely open-source and require a complex coupling scheme. To close this gap between "best"and "tractable"GIA models, we propose FastIsostasy here, a regional GIA model capturing lateral variations in the lithospheric thickness and mantle viscosity. By means of fast Fourier transforms and a hybrid collocation scheme to solve its underlying partial differential equation, FastIsostasy can simulate 100ĝ€¯000 years of high-resolution bedrock displacement in only minutes of single-CPU computation, including the changes in sea-surface height due to mass redistribution. Despite its 2D grid, FastIsostasy parameterises the depth-dependent viscosity and therefore represents the depth dimension to a certain extent. FastIsostasy is benchmarked here against analytical, as well as 1D and 3D numerical solutions, and shows good agreement with them. For a simulation of the last glacial cycle, its mean and maximal error over time and space respectively yield less than 5ĝ€¯% and 16ĝ€¯% compared to a 3D GIA model over the regional solution domain. FastIsostasy is open-source, is documented with many examples and provides a straightforward interface for coupling to an ice-sheet model. The model is benchmarked here based on its implementation in Julia, while a Fortran version is also provided to allow for compatibility with most existing ice-sheet models. The Julia version provides additional features, including a vast library of adaptive time-stepping methods and GPU support.