  Infinite horizon optimal stopping problems for a L\'evy processes with a
two-sided reward function are considered. A two-sided verification theorem is
presented in terms of the overall supremum and the overall infimum of the
process. A result to compute the angle of the value function at the optimal
thresholds of the stopping region is given. To illustrate the results, the
optimal stopping problem of a compound Poisson process with two-sided
exponential jumps and a two-sided payoff function is solved. In this example,
the smooth-pasting condition does not hold.
