This article reports a slow-light fiber-Bragg-grating (FBG) pressure sensor that functions both as a microphone and a hydrophone and pushes the limit of acoustic pressure resolution of conventional FBG sensors operated without external diaphragms. The sensor utilizes a narrow slow-light resonance to enhance its optical response (greater transmission change per wavelength shift), a soft polymeric coating to enhance its acoustic response (greater wavelength shift per pressure), and an ultranarrow linewidth laser to reduce its laser frequency noise (which often dominates in such sensors). The coated fiber microphone exhibits an average resolution of $\sim 210 ~\mu $ Pa/ $\surd $ Hz (100 Hz–10 kHz), which is ~6 times better than the previous record. When used as a hydrophone, the resolution is $\sim 880 ~\mu $ Pa/ $\surd $ Hz (1–100 kHz), which is better than the previous record for a passive FBG hydrophone by a factor of ~23 over the same acoustic frequency range. The wavelength shift per unit pressure is larger for the coated FBG than for the bare FBG by a measured factor of ~16 in air and ~3.7 in water. This last value differs markedly from a published ~300-fold enhancement using a conventional FBG hydrophone coated with the same polymer. It is shown that most of this discrepancy is due to a referencing error in the publication that reported this improvement. With further improvement, slow-light FBGs could be utilized for high-resolution applications, such as in the deep sea and seismic research.