This invention relates to the design and function of a compressible valve replacement prosthesis, collared or uncollared, which can be deployed into a beating heart without extracorporeal circulation using a transcatheter delivery system. The design as discussed focuses on the deployment of a device via a minimally invasive fashion and by way of example considers a minimally invasive surgical procedure preferably utilizing the intercostal or subxyphoid space for valve introduction. In order to accomplish this, the valve is formed in such a manner that it can be compressed to fit within a delivery system and secondarily ejected from the delivery system into the annulus of a target valve such as a mitral valve or tricuspid valve.