We demonstrate a mid-infrared dysprosium-doped fluoride fiber laser with a continuously tunable output range of 573 nm, pumped by a 1.7 μm Raman fiber laser. To the best of our knowledge, this represents the largest tuning range achieved to date from any rare-earth-doped fiber laser and, critically, spans the 2.8-3.4 μm spectral region, which contains absorption resonances of many important functional groups and is uncovered by other rare-earth ions. Output powers up to 170 mW are achieved, with 21% slope efficiency. We also discuss the relative merits of the 1.7 μm pump scheme, including possible pump excited-state absorption.