The use of expressive Virtual Characters is an effective complementary means of communication for social networks offering multi-user 3D-chatting environment. In such context the facial expression channel offers a rich medium to translate the on-going emotions conveyed by the text-based exchanges. However, until recently, only purely symmetric facial expressions have been considered for that purpose. In this article we examine human sensitivity to facial asymmetry in the expression of both basic and complex emotions. The rationale for introducing asymmetry in the display of facial expressions stems from two well established observations in cognitive neuroscience: first that the expression of basic emotions generally displays a small asymmetry, second that more complex emotions such as ambivalent feeling may reflect in the partial display of different, potentially opposite, emotions on each side of the face. A frequent occurrence of this second case results from the conflict between the truly felt emotion and the one that should be displayed due to social conventions. Our main hypothesis is that a much larger expressive and emotional space can only be automatically synthesized by means of facial asymmetry when modelling emotions with a general Valence-Arousal-Dominance dimensional approach. Besides, we want also to explore the general human sensitivity to the introduction of a small degree of asymmetry into the expression of basic emotions. We conducted an experiment by presenting 64 pairs of static facial expressions, one symmetric and one asymmetric, illustrating eight emotions (three basic and five complex ones) alternatively for a male and a female character. Each emotion was presented four times by swapping the symmetric and asymmetric positions and by mirroring the asymmetrical expression. Participants were asked to grade, on a continuous scale, the correctness of each facial expression with respect to a short definition. Results confirm the potential of introducing facial asymmetry for a subset of the complex emotions. Guidelines are proposed for designers of embodied conversational agent and emotionally-reflective avatars.