A point-absorber wave-energy extractor is developed, consisting of a dual coaxial-cylinder system, with the inner cylinder tension-tethered and an outer cylinder (floater) oscillating vertically. A permanent magnet linear generator (PMLG) is used as a power take-off (PTO) capturing wave energy from the relative motion of the two cylinders. The mathematical modeling of the system includes the coupling effects of the cylinder hydrodynamics and the PMLG behavior. It gives a rational and effective way of providing performance predictions and directions for optimization. The flat bottom shape of the floater is modified into a needle-like curved shape to minimize viscous losses, which leads to three-times increase in floater response, compared with the flat-bottom geometry and thus improved wave-energy capture. The behavior of the PTO in the presence of an appropriate supporting structure for the coaxial cylinders are investigated, and optimal operating conditions for energy extraction and mechanical to electrical conversion efficiency are determined. Experimental results of this coupled system in regular waves confirm the validity of the theoretical predictions and soundness of the engineering design. Optimizing the floater bottom shape and the operating conditions for energy extraction lead to a two-times increase in overall efficiency, even without any active control.