RECON will test the hypothesis that patients who have symptomatic, unilateral carotid artery occlusion and stage II cerebral hemodynamic failure as measured by increased oxygen extraction fraction (OEF) on positron emission tomography (PET) will have better cognitive function following EC-IC bypass when compared with an identical group of patients treated with best medical therapy alone.  We will test this hypothesis by conducting a randomized single-blinded prospective trial on 260 enrolled COSS patients randomized equally to surgical or non-surgical treatment.