Sometimes the same act causes both a good result and an evil result at the same time. The question for the moralist is “Should such an act be performed?” The answer is that is can be, but only if four conditions are met: First, the act itself must be good or indifferent. Second, the good effect must not be caused by the evil effect. Third, the good effect and not the evil effect must be directly intended by the agent. Forth, there must be a proportionality between the good and evil result (i.e., the good must outweigh the evil). An illustrative example would be the use of the opium derivative, morphine, to ease pain in terminal patients. It is known that this drug also decreases respiration, thus it may expedite the death of the patient. It is also highly addictive, which would render it inadvisable to give to patients likely to live, as they could become addicts. If the terminal patient is in severe pain and competent medical professionals have determined that death in immanent, then it is perfectly permissible to administer the morphine even though respiration could be decreased and death thus brought on quicker.
The first condition is met, as the administration of morphine is not an intrinsic evil. The second is met, as the pain is not mitigated through death or decreased respiration, but by the analgesic effect of the drug. The third condition would have to be in the mind of the health-care professional. As long as he had in mind the alleviation of pain and not the euthanising of his patient, he would fulfill this condition. Forth, the good of the mitigation of severe pain (which could, after all, lead the patient to theological despair) is commonly considered to outweigh the evil of a decreased respiration leading to a quicker death.
(For more on Double Effect see the this on-line article by a Catholic Psychiatrist.)