A variety of transmission mechanisms are provided that include 'radially inverted' pulleys that are nested within each other or otherwise overlap in order to exert 'inward' forces onto a compressive belt that transmits power between the pulleys. By exerted forces 'inward' onto the belt, the belt can be subjected to net compression everywhere along its length. This allows the belt to be less complex and to have a lower cost than belts of transmissions that exert forces 'outward' from pulleys onto a belt, thus requiring expensive and technically challenging belt packs or other elements to sustain the longitudinal tensions experienced by such belts, even when such belts are operated as "push" belts. Transmissions that include such 'radially inverted' pulleys can exhibit reduced size and cost and increased power capacity compared to transmissions that employ 'non-radially inverted' pulleys.