The paper describes steps in the development of a low Reynolds number second-moment closure for general flow geometries. This requirement means that the model cannot contain geometry-specific quantities, such as the wall-normal vector or wall distance. In their place, invariant dimensionless ''gradient indicators'' are introduced. New models are also devised for stress dissipation to capture the very diverse behaviour of the different components of epsilon(ij) in the wall's vicinity with and without shear. A novel decomposition of the fluctuating pressure terms is also proposed. Applications are shown for shear-free boundary regions, plane channel, and stagnation flows.