Strong enhancement of optoacoustic interactions in the micrometer-sized core of a photonic crystal fiber (PCF) enables stable, harmonic mode locking of a soliton fiber laser at GHz frequencies. Here we report that by tapering the PCF during the draw, the optoacoustic gain bandwidth can be broadened to similar to 47 MHz, more than 3 times wider than in the untapered fiber. This made possible broad pulse-repetition-rate tuning over 66 MHz (from 2.042 to 2.108 GHz) of an optoacoustically mode-locked soliton fiber laser. Within this tuning range, the harmonically mode-locked pulse trains at the laser output were observed to be quite robust, with better than 40 dB supermode suppression ratio, sub-ps pulse timing jitter, and <0.2% relative intensity noise. This gigahertz-rate, near-infrared soliton fiber laser has remarkable pulse-rate tunability and low noise level, and has important potential applications in frequency metrology, high-speed optical sampling, and fiber telecommunications. (C) 2019 Optical Society of America