Standard methods for artefact removal in MEG or EEG measurements consist of rejection of either corrupted epochs or signal space projection (SSP). We propose to combine the two methods by applying SSP only in corrupted epochs and thus using both temporal and spatial information. This partial signal space projection necessarily results in smaller variances for the source localization. Formulae for dipole localization errors as a function of fraction of corrupted epochs are derived and verified in Monte Carlo simulations of MEG measurements corrupted with eye artefacts. A theoretical analysis of various measuring devices, classes of artefact and locations of dipole of interest shows that the proposed method leads to significant improvement for frontal signal dipoles and for 30-80% corrupted epochs.