Context. CO and N2 are two abundant species in molecular clouds. CO molecules are heavily depleted from the gas phase towards the centre of pre-stellar cores, whereas N2 maintains a high gas phase abundance. For example, in the molecular cloud L183, CO is depleted by a factor of ≈400 in its centre with respect to the outer regions of the cloud, whereas N2 is only depleted by a factor of ≈20. The reason for this difference is not yet clear, since CO and N2 have identical masses, similar sticking properties, and a relatively close energy of adsorption. Aims. We present a study of the CO-N2 system in sub-monolayer regimes, with the aim to measure, analyse and elucidate how the adsorption energy of the two species varies with coverage, with much attention to the case where CO is more abundant than N2. Methods. Experiments were carried out using the ultra-high vacuum (UHV) set-up called VENUS. Sub-monolayers of either pure 13CO or pure 15N2 and 13CO:15N2 mixtures were deposited on compact amorphous solid water ice, and crystalline water ice. Temperature-programmed desorption experiments, monitored by mass spectrometry, are used to analyse the distributions of binding energies of 13CO and 15N2 when adsorbed together in different proportions. Results. The distribution of binding energies of pure species varies from 990 K to 1630 K for 13CO, and from 890 K to 1430 K for 15N2. When a CO:N2 mixture is deposited, the 15N2 binding energy distribution is strongly affected by the presence of 13CO, whereas the adsorption energy of CO is unaltered. Conclusions. Whatever types of water ice substrate we used, the N2 effective binding energy was significantly lowered by the presence of CO molecules. We discuss the possible impact of this finding in the context of pre-stellar cores.