A conjecture by Campana and Peternell says that if a positive multiple of KX is linearly equivalent to an effective divisor D plus a pseudo-effective divisor, then the Kodaira dimension of X should be at least as big as the Iitaka dimension of D. This is a very useful generalization of the non-vanishing conjecture (which is the case D = 0). I will explain why the Campana-Peternell conjecture is (almost?) equivalent to the non-vanishing conjecture, using recent work on singular metrics on pluri-adjoint bundles.