We consider a Faustmann timber harvesting problem arising in the literature on rational forest management by modeling the value of the harvested resource as a time homogeneous, regular, and linear diffusion. We state a set of easily veri. able general conditions under which the existence and uniqueness of an optimal cutting value and, consequently, an optimal impulse control, are guaranteed. We also present a set of conditions under which increased volatility increases both the value and the optimal harvesting threshold at which the irreversible harvesting strategy is exercised.