Conditional Average Treatment Effect (CATE) estimation, at the heart of counterfactual reasoning, is a crucial challenge for causal modeling both theoretically and applicatively, in domains such as healthcare, sociology, or advertising. Borrowing domain adaptation principles, a popular design maps the sample representation to a latent space that balances control and treated populations while enabling the prediction of the potential outcomes. This paper presents a new CATE estimation approach based on the asymmetrical search for two latent spaces called Asymmetrical Latent Representation for Individual Treatment Effect (ALRITE), where the two latent spaces are respectively intended to optimize the counterfactual prediction accuracy on the control and the treated samples. Under moderate assumptions, ALRITE admits an upper bound on the precision of the estimation of heterogeneous effects (PEHE), and the approach is empirically successfully validated compared to the state-of-the-art