  Let $(X, \Delta)$ be a projective klt pair of dimension $2$ and let $L$ be a
nef $\mathbb{Q}$-divisor on $X$ such that $K_X + \Delta + L$ is nef. As a
complement to the Generalized Abundance Conjecture by Lazi\'c and Peternell, we
prove that if $K_X + \Delta$ and $L$ are not proportional modulo numerical
equivalence, then $K_X + \Delta + L$ is semiample. An example due to Lazi\'c
shows that this is no longer true in any dimension $n \ge 3$.
