Introduction: The Circle of Willis (CoW) is the most effective collateral circulation to the brain during internal carotid artery (ICA) occlusion. Carotid stump pressure (CSP) is an established surrogate measure of the cerebral collateral circulation. This study aims to use hemodynamic and computed tomography angiography measurements to determine the strongest influences upon the dependent variable, CSP. These findings could help clinicians noninvasively assess the adequacy of the collateral circulation and facilitate surgical risk assessment in an outpatient setting. Methods: CSP and mean arterial pressure were measured during carotid endarterectomy or during carotid balloon test occlusion in 92 patients. Intracranial arterial diameters were measured on computed tomography angiography at 16 different locations. Univariate and multivariate analyses were used to determine the key factors associated with CSP. In a subgroup of individuals (n=27) with severe (>70% North American Symptomatic Carotid Endarterectomy Trial) contralateral stenosis or occlusion, the same analysis was performed. Results: The contralateral anterior cerebral artery proximal to anterior communicating artery (A1) of the CoW had the strongest influence upon CSP, followed by the mean arterial pressure, the contralateral ICA diameter, and the anterior communicating artery diameter (R2=0.364). In the subgroup with high-grade contralateral ICA stenosis, the ipsilateral posterior communicating artery exerted the strongest influence (R2=0.620). Conclusions: During ICA occlusion, the anterior CoW dominates in preserving collateral flow, especially the contralateral A1 segment. In individuals with high-grade contralateral carotid stenosis, the posterior communicating artery calibre becomes a dominant influence. The most favourable anatomy consists of large contralateral A1 and anterior communicating arteries, and no contralateral carotid stenosis.