To print accurate colours, every printing system needs to be characterised. Nowadays, this characterisation is performed by printing and measuring a colour target and creating an ICC profile. Every time the substrate or the ink changes, this procedure has to be repeated. In frequently changing environments, like the packaging industry, the standard colour characterisation procedure is too demanding in resources to be of any practical use.In this work, we present a novel technique that characterises the printing system without reprinting a colour target at each substrate or ink change. It requires the printing of a target only once per printer system and can handle an ink or a substrate change with an off-line spectral measurement of the new ink or substrate. This results in a substantial progress in terms of resource allocation and costs.To achieve our goal, we developed a new physical model of a printer. In addition, we needed an algorithm for modifying an existing ICC profile based on this model.