The coexistence of obstructive sleep apnea (OSA) and chronic obstructive pulmonary disease (COPD) has been described as the “overlap syndrome” (OS) [1]. Compared to patients with simple OSA, patients with OS exhibit a lower nocturnal oxygen saturation (SaO2), more profound desaturations during the apneic events and often severe hypoventilation particularly during rapid-eye-movements sleep [2].