  The expected present value of dividends is one of the classical stability
criteria in actuarial risk theory. In this context, numerous papers considered
threshold (refractive) and barrier (reflective) dividend strategies. These were
shown to be optimal in a number of different contexts for bounded and unbounded
payout rates, respectively. In this paper, motivated by the behaviour of some
dividend paying stock exchange companies, we determine the optimal dividend
strategy when both continuous (refractive) and lump sum (reflective) dividends
can be paid at any time, and if they are subject to different transaction
rates. We consider the general family of spectrally positive L\'evy processes.
Using scale functions, we obtain explicit formulas for the expected present
value of dividends until ruin, with a penalty at ruin. We develop a
verification lemma, and show that a two-layer (a,b) strategy is optimal. Such a
strategy pays continuous dividends when the surplus exceeds level a>0, and all
of the excess over b>a as lump sum dividend payments. Results are illustrated.
