The present disclosure is drawn to methods for oxidatively bleaching or coloring hair. The methods employ a fortifying composition and a conditioning composition, which are used in various routines. Treating hair according to the routines prevent, minimize, or mitigate damage to the hair caused by the oxidative bleaching or coloring process. The fortifying composition includes: (a) citric acid, a salt thereof, or a combination thereof; (b) cyclodextrin, a salt thereof, or a combination thereof; (c) one or more polyols; and (d) water. The conditioning composition includes: (a) one or more cationic surfactants; (b) one or more non-silicone fatty compounds; (c) one or more silicone oils; and (d) and water. The methods strengthen the hair, improve curl retention of the hair, prevent frizz of the hair, and remediate damage to the hair caused by chemical bleaching or coloring of the hair.