Asymmetry in contrarian behavior is investigated within the Galam model of opinion dynamics using update groups of size 3 with two competing opinions A and B. Denoting $x$ and $y$ the respective proportions of A and B contrarians, fourschemes of implementations are studied. First scheme activates contrarians after each series of updates with probabilities $x$ and $y$ for agents holding respectively opinion A and B. Second scheme activates contrarians within the groups after the update only against the global majority opinion. Third scheme considers in-group contrarians acting prior to the local update against both majority and minority opinions. Last scheme considers asymmetric in-group contrarians acting prior to the update only against majority opinion. The main result is the loss of the fifty-fifty attractor produced by symmetric contrarians together with a much richer variety of dynamics.