A process for altering the appearance of hair, the process comprising the steps of (a) providing a composition for dyeing and reducing curl and/or frizziness of hair, said composition comprising, in a cosmetically acceptable carrier: (i) at least one non-hydroxide base; (ii) at least one protein denaturant different from (a)(ii); (iii) at least one direct dye; (iv) at least one thickening agent; (v) optionally, at least one alkoxysilane comprising at least one solubilizing functional group; and (vi) optionally, at least one fatty substance; (b) contacting the hair with the composition in (a) to form treated hair; (c) smoothing the treated hair using a combination of heat and means for physically smoothing hair to form smoothed hair; (d) optionally, shampooing the smoothed hair; and (e) rinsing the smoothed hair.