Radiative transfer is sufficiently well understood that its parameterization in atmospheric models is primarily an effort to balance computational cost and accuracy. The most common approach is to compute radiative transfer with the highest practical spectral accuracy but infrequently in time and/or space, though errors introduced by this approximation are difficult to quantify. An alternative is to perform spectrally sparse calculations frequently in time using randomly chosen spectral quadrature points. Here we show that purely random quadrature points, though effective in some large-eddy simulations, are not a good choice for models in which the land surface responds to radiative fluxes because surface temperature perturbations can be large enough, and persistent long enough, to affect model evolution. These errors may be mitigated by choosing teams of spectral points designed to limit the maximum surface flux error; teams, rather than individual quadrature points, are then chosen randomly. The approach is implemented in the ECHAM6 global model and the results are examined using “perfect-model” experiments on time scales ranging from a day to a month. In this application the approach introduces errors commensurate with the infrequent calculation of broadband calculations for the same computational cost. But because teams need not increase with size, and indeed may become better and more balanced with increased spectral density, improvements in radiative transfer may not need to be traded off against spatiotemporal sampling.