The mini-pill is also called POP: Progestin-Only Pill.
The mini-pill consists solely of progestin and is taken continuously. It’s less reliable than other oral contraceptives. The pills must be taken at precisely the same time every day to maintain effectiveness. So you have to be very motivated when you decide this is your method of birth control. If you deviate from the schedule for three hours the pill is not reliable anymore.
The first month the mini-pill is not reliable. You have to use condoms as a back-up.
POP’s can be taken by women who are at risk of uterine or breast cancer, have a history of blood clots, have migraine, are heavy smokers over the age of 35 or have an active liver disease. It is also a good method for women who are breastfeeding.
A few Brands: Cerazette, Plan B, Micronor, Nor-QD, Ovrette.

See also: other 'progestin only' methods of birth control