  We consider a class of two-sided singular control problems. A controller
either increases or decreases a given spectrally negative Levy process so as to
minimize the total costs comprising of the running and control costs where the
latter is proportional to the size of control. We provide a sufficient
condition for the optimality of a double barrier strategy, and in particular
show that it holds when the running cost function is convex. Using the
fluctuation theory of doubly reflected Levy processes, we express concisely the
optimal strategy as well as the value function using the scale function.
Numerical examples are provided to confirm the analytical results.
