In this paper, we consider a parametric density contamination model. We work with a sample of i.i.d. data with a common density, $f^\star =(1-λ^\star) φ+ λ^\star φ(.-μ^\star)$, where the shape $φ$ is assumed to be known. We establish the optimal rates of convergence for the estimation of the mixture parameters $(λ^\star,μ^\star)$. In particular, we prove that the classical parametric rate $1/\sqrt{n}$ cannot be reached when at least one of these parameters is allowed to tend to $0$ with $n$.