Scalp electroencephalograms (EEG) are susceptible to cranial and cervical muscle contamination from frequencies as low as 20 hertz, even in relaxed conditions. Reliably recording cognitive activity, which is in this range, is impossible without removing or reducing the effect of muscle contamination. Our unique database of paralysed conscious subjects enabled us to test the effect of combining beamforming and blind source separation in reducing tonic muscle contamination of scalp electrical recordings. Using the beamforming technique, muscle sources are separated automatically based on their location; while using blind source separation, muscle components are separated based on their spectral gradient. Our results show that applying the beamforming technique on data pruned by a blind source separation technique (or vice versa) can reduce tonic muscle contamination significantly more than applying either of them separately, especially at peripheral locations. Hence, these approaches complement each other in reducing muscle contamination of EEG.