  We consider the multi-refraction strategies in two equivalent versions of the
optimal dividend problem in the dual (spectrally positive L\'evy) model. The
first problem is a variant of the bail-out case where both dividend payments
and capital injections must be absolutely continuous with respect to the
Lebesgue measure. The second is an extension of Avanzi et al. [4] where a
strategy is a combination of two absolutely continuous dividend payments with
different upper bounds and different transaction costs. In both problems, it is
shown to be optimal to refract the process at two thresholds, with the
optimally controlled process being the multi-refracted L\'evy process recently
studied by Czarna et al. [9]. The optimal strategy and the value function are
succinctly written in terms of a version of the scale function. Numerical
results are also given.
