We analyse the properties of dark matter haloes in the cold-plus-warm dark matter (CWDM) cosmologies. We study their dependence on the fraction and velocity dispersion of the warm particle, keeping the free-streaming scale fixed. To this end, we consider three models with the same free-streaming: (1) a mixture of 90 per cent of CDM and 10 per cent of WDM with the mass 1 keV; (2) a mixture of 50 per cent of CDM and 50 per cent of WDM with the mass 5 keV and (3) pure WDM with the mass 10 keV. 'Warm' particles have rescaled –Dirac spectrum of primordial velocities (as non-resonantly produced sterile neutrinos would have). We compare the properties of haloes among these models and with a ΛCDM with the same cosmological parameters. We demonstrate that although these models have the same free-streaming length and the suppression of matter spectra are similar at scales probed by the Lyman α forest (comoving wave-numbers k < 3–5 h Mpc−1), the resulting properties of haloes with masses below ∼1011 M⊙ are different due to the different behaviour of matter power spectra at smaller scales. In particular, we find that while the number of galaxies remains the same as in the ΛCDM case, their density profiles become much less concentrated and hence in better agreement with current observational constraints. Our results imply that a single parameter (e.g. free-streaming length) description of these models is not enough to fully capture their effects on the structure formation process.