The Fontan procedure is employed as the final-stage palliation in single-ventricle congenital heart patients and results in diversion of venous blood directly to the pulmonary arteries. Fontan patients have been known to suffer from postoperative systemic venous hypertension, which in turn is associated with pleural effusions and protein losing enteropathy, leading to a decreased duration and quality of life. Despite the ongoing debate on its benefits, a circular fenestration hole (typically 4 mm) establishing a venous shunt to the common atrium is traditionally employed to relieve venous pressure in the Fontan conduit and improve early postoperative Fontan hemodynamics. However, these improvements come at the cost of reduced oxygen saturation due to excessive right-to-left shunting if the fenestration is permanent. The ideal “selective” fenestration would therefore limit or eliminate shunt flow at tolerable systemic venous pressures and allow increased flow at high pressures. The objective of this study is to introduce new fenestration designs that exhibit these desirable pressure-flow characteristics. Novel plus-shaped and S-shaped fenestration designs with leaflets are introduced as alternatives to the traditional circular fenestration, each having identical effective orifice areas at the fully open states. In vitro steady leakage flow tests were performed for physiological flow-driving pressures in order to obtain pressure-drop versus flow-rate characteristics. In addition, the leaflet opening kinematics of the plus-shaped fenestration was investigated computationally using finite element simulation. Fluid-structure interaction analysis was performed to determine leaflet displacements and pressure-flow characteristics at low pressures. Further, a lumped parameter model of the single-ventricle circuit was created to simulate pulsatile flow conditions For the plus-shaped fenestration, the flow rate was found to increase nonlinearly with increased driving systemic venous pressures at high physiological-pressure drops which did not cause the leaflets to fully open, and linearly for low driving pressures. These results indicate that leaflets of the plus-shaped fenestration design activated passively after a critical systemic venous pressure threshold. This feature is ideal for minimizing undesirable excessive venous shunting. A large variability in shunting flow rate may be obtained by changing the shape, thickness, size, and material of the fenestration to suit requirements of the patient, which can further limit shunt flow in a controlled manner.