In this paper we compare various preconditioners for the numerical solution of partial dierential equations. We compare a coarse grid correction preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the de ated preconditioned system is always, i.e. for all deflation vectors and all restrictions and prolongations, below the condition number of the system preconditioned by the coarse grid correction. This implies that the Conjugate Gradient method applied to the de ated preconditioned system converges always faster than the Conjugate Gradient method applied to the system preconditioned by the coarse grid correction. Numerical results for porous media flows emphasize the theoretical results.