Sleep disturbances after ischaemic stroke include alterations of sleep architecture, obstructive sleep apnea, restless legs syndrome, daytime sleepiness and insomnia. Our aim was to explore their impacts on functional outcomes at month 3 after stroke, and to assess the benefit of continuous positive airway pressure in patients with severe obstructive sleep apnea. Ninety patients with supra-tentorial ischaemic stroke underwent clinical screening for sleep disorders and polysomnography at day 15 ± 4 after stroke in a multisite study. Patients with severe obstructive apnea (apnea-hypopnea index ≥ 30 per hr) were randomized into two groups: continuous positive airway pressure-treated and sham (1:1 ratio). Functional independence was assessed with the Barthel Index at month 3 after stroke in function of apnea-hypopnea index severity and treatment group. Secondary objectives were disability (modified Rankin score) and National Institute of Health Stroke Scale according to apnea-hypopnea index. Sixty-one patients (71.8 years, 42.6% men) completed the study: 51 (83.6%) had obstructive apnea (21.3% severe apnea), 10 (16.7%) daytime sleepiness, 13 (24.1%) insomnia, 3 (5.7%) depression, and 20 (34.5%) restless legs syndrome. Barthel Index, modified Rankin score and Stroke Scale were similar at baseline and 3 months post-stroke in the different obstructive sleep apnea groups. Changes at 3 months in those three scores were similar in continuous positive airway pressure versus sham-continuous positive airway pressure patients. In patients with worse clinical outcomes at month 3, mean nocturnal oxygen saturation was lower whereas there was no association with apnea-hypopnea index. Poorer outcomes at 3 months were also associated with insomnia, restless legs syndrome, depressive symptoms, and decreased total sleep time and rapid eye movement sleep.