A subtalar joint prosthesis that is adapted to replace the natural subtalar joint that exists between a patient's talus and calcaneus bones includes talar and calcaneal components. Each of these is configured to have a shape that is herein defined as being a portion of the boundary surface of a frustum. Meanwhile, these components' inner surfaces are configured to: (a) generally follow the anatomic contour of the original joint surface to which each component is to be attached, and (b) minimize each components's average thickness, consistent with providing sufficient strength and rigidity for the components, so as to require minimum bone resection for the implantation of these components.