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A capacitor-driven pulsed magnet coil has been designed to generate fields in the 70-75 T range, with a life expectancy of at least 100 pulses, thus qualifying as a '75 T class user magnet'. The bore is 10 mm and the rise time used in our experiments is 4 ms. The coil consists of two coaxial sections: the inner section, where stresses are highest, is made with CuNb microcomposite wire and optimized Zylon reinforcement; the outer section is made with soft copper and glass fibre composite. In the inner section, the stress in each layer is self-contained, while the stresses induced in the outer section are transmitted to a thick shell made from steel and carbon fibre composite. The cross section of the copper wires is adjusted to redistribute the heating evenly between the inner and the outer section. Another innovative design feature is a system for axial compression that can be easily retightened during coil training. Two nearly identical coils were manufactured and tested to 72 T; this is a limit imposed due to overheating when using our 10 kV, 0.5 MJ capacitor bank (at an energy of 380 kJ). At 75 T, the calculated von Mises stress in the Zylon composite is 2.6 GPa, well below the UTS of more than 3 GPa, and the CuNb wire is still in an elastic state.