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.