We discuss a fiber-integrated refractive index sensor with strongly improved detection performance. The resonator has been implemented by means of focused-ion beam milling of a step index fiber and shows a sensitivity of about 1.15µm/RIU. Coating the resonator walls led to a strongly improved mirror reflectivity by a factor of about 26. Design rules for device optimization and a detailed mathematical analysis are discussed, revealing that the sensor operates as an optimized Fabry-Perot resonator. We also show that the performance of such kind of Fabry-Perot sensors is, in general, limited by the detection limit function – a quantity depending on the cavitiy’s finesse and on the measurement capabilities used.