This study will examine the effect of three weeks vs. six weeks of CPAP treatment on cognitive functioning and sleep in patients with Parkinson's disease and sleep apnea. It is designed as a randomized, double blind, placebo-controlled trial of CPAP. As a comparison group, half the patients will first be randomly assigned to three weeks of shamCPAP, followed by three weeks of therapeutic CPAP treatment. Sleep, functional outcome and mood questionnaires and a repeatable neuropsychological test battery, chosen to be sensitive to the type of changes we expect to find in memory and cognitive function, will be administered before the start of treatment, after three weeks, and after six weeks of treatment.