We revisit the dividend payment problem in the dual model of Avanzi et al. (, , and ). Using the fluctuation theory of spectrally positive Lévy processes, we give a short exposition in which we show the optimality of barrier strategies for all such Lévy processes. Moreover, we characterize the optimal barrier using the functional inverse of a scale function. We also consider the capital injection problem of  and show that its value function has a very similar form to the one in which the horizon is the time of ruin.