We consider optimal conservation strategies for a population whoseviability is affected both by an alien species (e.g. a competitor, apredator, or a pathogen) and by a random fluctuation of the environment(e.g. humidity). We assume that the survivorship of the endangeredpopulation can be improved by a conservation effort, but also by anextermination effort that decreases the density of the alien species.Both efforts decrease the extinction probability of the endangeredpopulation, but they are accompanied by economic costs. We assume thatthe optimal strategy minimizes the weighted sum of the extinctionprobability and the economic costs. We derive necessary conditions forthe optimal conservation and/or extermination efforts to be positiveand obtain the optimal effort levels. We also examine the effect oflack of information on the impact of the alien species on optimaleffort levels