The present invention concerns a non-toxic solid pharmaceutical composition for oral administration, containing one or more cysteine compounds from the group of L-cysteine, D-cysteine and N-acetyl cysteine, combined with one or more additional active agents, at least one of which being selected from cystine, glutathione and methionine, the composition further containing one or more pharmaceutical additives. Further, the invention concerns a method for reducing the incidence of severe headaches, particularly migraine and/or cluster headaches.