Based on the TenStream solver, we present a new method to accelerate 3D radiative transfer towards the speed of currently used 1D solvers. Using a shallow-cumulus-cloud time series, we evaluate the performance of this new solver in terms of both speed and accuracy. Compared to a 3D benchmark simulation, we show that our new solver is able to determine much more accurate irradiances and heating rates than a 1D δ-Eddington solver, even when operated with a similar computational demand.