We consider the question of stabilization for the damped wave equation on tori (∂^2_t−Δ)u+a(x)∂_t u=0. When the damping coefficient $a(x)$ is continuous the question is quite well understood and the geometric control condition is necessary and sufficient for uniform (hence exponential) decay to hold. When $a(x)$ is only $L^{\infty}$ there are still gaps in the understanding. Using second microlocalization we completely solve the question for damping coefficients of the form a(x)=∑_{i=1}^J a_j 1_{x∈R_j}, where $R_j$ are cubes. This is a joint work with P. Gérard.