(1) Background: Polymeric heart valves are prostheses constructed out of flexible, synthetic materials to combine the advantageous hemodynamics of biological valves with the longevity of mechanical valves. This idea from the early days of heart valve prosthetics has experienced a renaissance in recent years due to advances in polymer science. Here, we present progress on a novel, 3D-printable aortic valve prosthesis, the TIPI valve, removing the foldable metal leaflet restrictor structure in its center. Our aim is to create a competitive alternative to current valve prostheses made from flexible polymers. (2) Methods: Three-dimensional (3D) prototypes were designed and subsequently printed in silicone. Hemodynamic performance was measured with an HKP 2.0 hemodynamic testing device using an aortic valve bioprosthesis (BP), a mechanical prosthesis (MP), and the previously published prototype (TIPI 2.2) as benchmarks. (3) Results: The latest prototype (TIPI 3.4) showed improved performance in terms of regurgitation fraction (TIPI 3.4: 15.2 ± 3.7%, TIPI 2.2: 36.6 ± 5.0%, BP: 8.8 ± 0.3%, MP: 13.2 ± 0.7%), systolic pressure gradient (TIPI 3.4: 11.0 ± 2.7 mmHg, TIPI 2.2: 12.8 ± 2.2 mmHg, BP: 8.2 ± 0.9 mmHg, MP: 10.5 ± 0.6 mmHg), and effective orifice area (EOA, TIPI 3.4: 1.39 cm2, TIPI 2.2: 1.28 cm2, BP: 1.58 cm2, MP: 1.38 cm2), which was equivalent to currently used aortic valve prostheses. (4) Conclusions: Removal of the central restrictor structure alleviated previous concerns about its potential thrombogenicity and significantly increased the area of unobstructed opening. The prototypes showed unidirectional leaflet movement and very promising performance characteristics within our testing setup. The resulting simplicity of the shape compared to other approaches for polymeric heart valves could be suitable not only for 3D printing, but also for fast and easy mass production using molds and modern, highly biocompatible polymers.