A hair dyeing process for improved and milder dyeing of hair, especially human hair. The ready-to-use dyeing composition comprises carboxylic acids in addition to dyeing agents and oxidizing agents in order to improve dyeing efficiency with less loss of natural hair properties. A process comprises applying onto hair a ready-to-use composition obtained by mixing compositions A comprising one or more hair dyes and one or more alkalising agents and having a pH of 7.5 to 12, B being an aqueous composition comprising one or more oxidising agents and having a pH of 1.5 to 5 and C comprising (i) one or more carboxylic acids or salts thereof having 3 or more carboxyl groups and (ii) one or more additional organic acids and/or salts thereof having one or two carboxyl groups. Composition C comprises (i) and (ii) at a concentration of 10 to 100% by weight. The ready-to-use composition has a pH of 8 to 11, comprises (i) and (ii) at a concentration of 1 to 10% by weight and is prepared by mixing A, B and C in a weight ratio in the range of 1:2:0.2 to 1:1:1. A kit for hair comprises compositions A, B and C.