This paper describes the results of work carried out on characterising desktop colour printers which do not enable the control of device colorant amounts independently and individually. As this particular limitation is shared by the majority of colour printers available to date, their characterisation is important especially in light of the development of gamut mapping algorithms. Four characterisation models have been implemented and tested for this purpose: a third order masking model, a model using separate masking equations for different parts of the colour space, a fourth order masking model and a model using distance weighted interpolation. The results of the experiments described in this paper suggest that the fourth order masking model is most suitable for the reproduction of complex images.