Summary: In this paper, we consider a parametric density contamination model. We work with a sample of i.i.d. data with a common density, \(f^{\star }=(1-\lambda^{\star })\phi +\lambda^{\star }\phi (\cdot-\mu^{\star })\), where the shape \(\phi\) is assumed to be known. We establish the optimal rates of convergence for the estimation of the mixture parameters \((\lambda^{\star },\mu^{\star })\in (0,1)\times \mathbb{R}^d \). 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 \(n \to \infty\).