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Starting birth control pills later than 1-3 days after your periods might cause problems with hormonal levels and efficacy of the birth control. In such cases, you should use back-up form of contraception (condom/spermicide) if having intercourse.
Consider visiting your gynecologist if you had altered periods (change in bleeding pattern and duration) in your last periods. Always start birth control at the instructed time to have full benefit from its use.
Take care.