We study the performance of an algebraic multigrid (AMG) preconditioner combined with conjugate gradient-type methods for the pressure equation in the presence of strong discontinuity of the permeability. Such discontinuities are problematic for iterative solvers, due to the dependence of the condition number of the discretized linear system of equations on the magnitude of the discontinuities. We identify two separate causes of such ill-conditioning, and assess how well the AMG preconditioner handles these. For the more difficult problems, we discuss techniques to modify the model to allow iterative solutions.