I just remembered that the lower dose continuous birth control pill is called Seasonique, which I believe just went generic a few months ago. You can choose to have periods or continue without them based on your choice.
Yes, there are a few birth control pills that do not cause headaches/migraines. These type of pills are continuous without periods. They are safe and have been on the market for years but are not used as much because some thought it was bad not to have a period every month. That myth has now been disproved, in fact when you take the pill with a 7 day break it is not really a period but withdrawal bleeding. In the USA it goes by names such as Lybrel (made by Wyeth). If you are outside the USA then you can Google it to find what name it might go by in your country. This type of regime is commonly used to circumvent headaches.migraines, and other period based problems in women, as it stops hormonal fluctuations from occurring.
I hope this helps.