Infrared (1.0-3.4-mu-m) recombination lines of six WC stars are analysed following the method of Hummer, Barlow & Storey. Improved spectral resolution and increased wavelength coverage give more consistent abundance estimates, for a larger number of recombination lines, compared to previous studies. Some low-energy-level transitions are found to be optically thick or formed through other processes. There is a clear decrease of derived ionic abundances with wavelength, attributed to an increase in continuous free-free opacity. Based on this observation, it is shown that the ionization stratification of the wind can be estimated, and that C/He abundance ratios can be reliably determined by defining a zone in the stellar wind, the same for all ions, in which ionic abundances are derived, thus overcoming previous difficulties inherent in the method. The derived C/He ratios range from 0.07 (WC9) to 0.41 (WC5), confirming a trend with WC subtype (ionization degree) for our small sample, with however the exception of the anomalous star WR 146, which has a low C/He ratio and a very high ionization degree. The C++++/He++ ratio is found to provide a good estimate of the C/He ratio.