The invention concerns a colour ink-jet printer comprising at least four ink cartridges (2) containing each one basic colour selected among yellow, magenta, cyan and black and at least one additional cartridge, and processing means (3,7) adapted to receive a printing order (4) containing data concerning the requested colour (CD) and/or the number and the colour of the ink droplets (ED) to be deposited on one another at a specific location called pixel (Pi) of a selected printing substrate. The processing means (3,7) include an optimizing mode capable of matching the requested colour (CD) and/or the required number and colour of droplets to be superimposed (ED) to obtain a selected colour in a given pixel (Pi) with an equivalent colour (CE) and/or an equivalent number and/or a colour of droplets to be superimposed to obtain a substantially equivalent and satisfactory colour rendering (CE) in conformity with the human eye sensory response, and of applying to the printer (1) the equivalent colour (CE) and/or the equivalent number and colour of droplets to be superimposed (EE) thus determined for each printing order received.