(WebMD) - Researchers Say More Tannins May Mean More Headache Pain. Many migraine sufferers find that the pleasure of a having a glass of red wine is soon followed by the pain of a headache. Now a small new study suggests that when it comes to migraines, some types of red wine may be more likely to trigger a headache than others. "My suggestion is the more tannins the wine has, [the] more migraine attacks it triggers," says researcher Abouch V. Krymchantowski, MD, PhD, of the Rio Headache Center in Rio de Janeiro, Brazil, in an email to WebMD.