  We consider de Finetti's stochastic control problem when the (controlled)
process is allowed to spend time under the critical level. More precisely, we
consider a generalized version of this control problem in a spectrally negative
L\'evy model with exponential Parisian ruin. We show that, under mild
assumptions on the L\'evy measure, an optimal strategy is formed by a barrier
strategy and that this optimal barrier level is always less than the optimal
barrier level when classical ruin is implemented. Also, we give necessary and
sufficient conditions for the barrier strategy at level zero to be optimal.
