Despite being vital in treating intensive-care patients with lung failure, especially COVID-19 patients, Veno-Venous Extra-Corporeal Membrane Oxygenation does not exploit its full potential, leaving ample room for improvement. The objective of this study is to determine the effect of cannula positioning and blood flow on the efficacy of Veno-Venous Extra-Corporeal Membrane Oxygenation, in particular in relationship with blood recirculation. We performed 98 computer simulations of blood flow and oxygen diffusion in a computerized-tomography-segmented right atrium and venae cavae for different positions of the returning and draining cannulae and ECMO flows of 3 L/min and 5\,\hbox {L}/\hbox {min}. For each configuration we measured how effective Veno-Venous Extra-Corporeal Membrane Oxygenation is at delivering oxygen to the right ventricle and thus to the systemic circulation. The main finding is that VV-ECMO efficacy is largely affected by the ECMO flow (global peak blood saturation: {92.8}\,\%; average inter-group saturation gain: 9 percentage points) but only scarcely by the positioning of the cannulae (mean saturation ± standard deviation for the 3 L/min case: 83.12 \pm 0.49; for the 5\,\hbox {L}/\hbox {min} case: 92.21 \pm 0.37). An important secondary outcome is that recirculation, more intense with a higher ECMO flow, is less detrimental to the procedure than previously thought. The efficacy of current ECMO procedures is intrinsically limited and fine-tuning the positions of the cannulae, risking infections, offers very little gain. Setting a higher ECMO flow offers the biggest benefit despite mildly increasing blood recirculation.