We analyse the skewness of the line-of-sight velocity distributions in model elliptical galaxies built through collisionless galaxy mergers. We build the models using large N-body simulations of mergers between either two spiral or two elliptical galaxies. Our aim is to investigate whether the observed ranges of skewness coefficient (h3) and the rotational support (V/σ), as well as the anticorrelation between h3 and V, may be reproduced through collisionless mergers. Previous attempts using N-body simulations failed to reach V/σ ~ 1-2 and corresponding high h3 values, which suggested that gas dynamics and ensuing star formation might be needed in order explain the skewness properties of ellipticals through mergers. Here we show that high V/σ and high h3 are reproduced in collisionless spiral-spiral mergers whenever a central bulge allows the discs to retain some of their original angular momentum during the merger. We also show that elliptical-elliptical mergers, unless merging from a high-angular momentum orbit, reproduce the strong skewness observed in non-rotating, giant, boxy ellipticals. The behaviour of the h3 coefficient therefore associates rapidly-rotating discy ellipticals to disc-disc mergers, and associates boxy, slowly rotating giant ellipticals to elliptical-elliptical mergers, a framework generally consistent with the expectations of hierarchical galaxy formation.