Our purpose in this work is to demonstrate that the efficiency of dose-rate computations in 125I brachytherapy, using multigroup discrete ordinates radiation transport simulations, can be significantly enhanced using broad energy group cross sections without a loss of accuracy. To this end, the DANTSYS multigroup discrete ordinates neutral particle transport code was used to estimate the absorbed dose-rate distributions around an 125I-model 6702 seed in two-dimensional (2-D) cylindrical R-Z geometry for four different problems spanning the geometries found in clinical practice. First, simulations with a high resolution 210 energy groups library were used to analyze the photon flux spectral distribution throughout this set of problems. These distributions were used to design an energy group structure consisting of three broad groups along with suitable weighting functions from which the three-group cross sections were derived. The accuracy of 2-D DANTSYS dose-rate calculations was benchmarked against parallel Monte Carlo simulations. Ray effects were remedied by using the DANTSYS internal first collision source algorithm. It is demonstrated that the 125I primary photon spectrum leads to inappropriate weighting functions. An accuracy of +/-5% is achieved in the four problem geometries considered using geometry-independent three-group libraries derived from either material-specific weighting functions or a single material-independent weighting function. Agreement between Monte Carlo and the three-group DANTSYS calculations, within three standard Monte Carlo deviations, is observed everywhere except for a limited region along the Z axis of rotational symmetry, where ray effects are difficult to mitigate. The three-group DANTSYS calculations are 10-13 times faster than ones with a 210-group cross section library for 125I dosimetry problems. Compared to 2-D EGS4 Monte Carlo calculations, the 3-group DANTSYS simulations are a 100-fold more efficient. Provided that these efficiency gains can be sustained in three-dimensional geometries, the results suggest that discrete ordinates simulations may have the potential to serve as an efficient and accurate dose-calculation algorithm for low-energy brachytherapy treatment planning.