A structure and method provide cables of high-temperature superconducting flat tape and/or filament wires, with a small bending diameter. A cable has a former having cross section that includes a rectangle having rounded ends (i.e. an obround), and the flat tape is wound around the surface of the former at an angle to minimize bending. The former surface may have raised helical ribs or lowered grooves to provide tape registration in multi-layer configurations. Tape may be wound from a spool onto the former under tension, and cut with a laser cutter to produce fine filaments immediately before winding. The former may be slit longitudinally to prevent loop eddy currents and reduce AC losses. The wound cable may be jacketed to provide a cable-in-conduit conductor (CICC), and coolant channels may be provided in the jacket or in the former.