We investigate the role of asymmetries in the line spread function of the 2-degree field (2dF) spectrograph and the variations in these asymmetries with the CCD, the plate, the time of observation, and the fibre. A data-reduction pipeline is developed that takes these deformations into account for the calibration and cross-correlation of the spectra. We show that, using the emission lines of calibration lamp observations, we can fit the line spread function with the sum of two Gaussian functions representing the theoretical signal and a perturbation of the system. This model is then used to calibrate the spectra and generate templates by downgrading high-resolution spectra. Thus, we can cross-correlate the observed spectra with templates degraded in the same way. Our reduction pipeline is tested on real observations and provides a significant improvement in the accuracy of the radial velocities obtained. In particular, the systematic errors that were as high as ∼20 km s−1 when applying the AAO reduction package 2DFDR are now reduced to ∼5 km s−1. Even though the 2dF spectrograph is to be decommissioned at the end of 2005, the analysis of archival data and previous studies could be improved by the reduction procedure we propose here.