In this paper, we study gain attenuation of linear systems subject to input saturation $\dot x=Ax+b\sg(u)$. In case there exists a family $\cal{K}$ of stabilizing feedback, we address the issue of estimating the infimum of $\gamma_k$, the gain of the output map $v\mapsto x_v$, defined for $k\in {\cal{K}}$, and where $x_v$ is the solution of $\dot x=Ax+b\sg(k(x)+v)$ starting at zero. For the 2D oscillator and double integrator, we explicitely determine an appropriate family $\cal{K}$ of stabilizing feedback and prove that the infimum over the gains is equal to zero.