Several lines of evidence suggest that as dark matter haloes grow their scale radius increases, and that the density in their central region drops. Major mergers seem an obvious mechanism to explain both these phenomena, and the resulting patterns in the concentration-mass-redshift relation. To test this possibility, we have simulated equal-mass mergers between haloes with a variety of cosmological density profiles, placed on various different orbits. The remnants typically have higher densities than the initial conditions, but differ only slightly from self-similar scaling predictions. They are reasonably well fit by Einasto profiles, but have parameters distinct from those of the initial conditions. The net internal energy available to the merger remnant, relative to the internal energy of the initial conditions, kappa, has the greatest influence on the properties of the final mass distribution. As expected, energetic encounters produce more extended remnants while mergers of strongly bound systems produce compact remnants. Surprisingly, however, the scale radius of the density profile shows the opposite trend, increasing in the remnants of low-energy encounters relative to energetic ones. Also even in the most energetic encounters, the density within the scale radius decreases only slightly (by 10-20 per cent), while for very low-energy systems it increases significantly after the merger. We conclude that while major mergers can produce remnants that are more diffuse at large radii, they are relatively ineffective at changing the central densities of haloes, and seem unlikely to explain the mean trends in the concentration-mass-redshift relation.