This study will determine if mirtazapine, a unique antidepressant that does not disturb sleep, will improve obstructive sleep apnea (OSA). The design is randomized, crossover, double blind, and placebo controlled. On two consecutive nights of one week, the patients receive either 30 mg mirtazapine or placebo at bedtime. The following week, the alternative medication is administered. The patients have known mild to moderate sleep apnea. The endpoints of the study are the apnea + hypopnea index (AHI), sleep quality, and the degree of arterial oxygen desaturation.