The finding that photographic and digital composites (blends) of faces are considered to be attractive has led to the claim that attractiveness is averageness. This would encourage stabilizing selection, favouring phenotypes with an average facial structure. The 'averageness hypothesis' would account for the low distinctiveness of attractive faces but is difficult to reconcile with the finding that some facial measurements correlate with attractiveness. An average face shape is attractive but may not be optimally attractive. Human preferences may exert directional selection pressures, as with the phenomena of optimal outbreeding and sexual selection for extreme characteristics. Using composite faces, we show here that, contrary to the averageness hypothesis, the mean shape of a set of attractive faces is preferred to the mean shape of the sample from which the faces were selected. In addition, attractive composites can be made more attractive by exaggerating the shape differences from the sample mean. Japanese and caucasian observers showed the same direction of preferences for the same facial composites, suggesting that aesthetic judgements of face shape are similar across different cultural backgrounds. Our finding that highly attractive facial configurations are not average shows that preferences could exert a directional selection pressure on the evolution of human face shape.