High-power tunable femtosecond mid-infrared (MIR) pulses are of great interest for many scientific and industrial applications. Here we demonstrate a compact fluoride-fiber-based system that generates single solitons tunable from 3 to 3.8 μm. The system is composed of an Er:ZBLAN fiber oscillator and amplifier followed by a fusion-spliced Dy:ZBLAN fiber amplifier. The Er:ZBLAN fiber amplifier acts as a power booster as well as a frequency shifter to generate Raman solitons up to 3 μm. The Dy:ZBLAN fiber amplifier transfers the energy from the residual 2.8 μm radiation into the Raman solitons using an in-band pumping scheme, and further extends the wavelength up to 3.8 μm. Common residual pump radiation and secondary solitons accompanying the soliton self-frequency shift (SSFS) are recycled to amplify Raman solitons, consequently displaying a higher output power and pulse energy, a wider shifting range, and an excellent spectral purity. Stable 252 fs pulses at 3.8 μm with a record average power of 1.6 W and a pulse energy of 23 nJ are generated. This work provides an effective way to develop high-power widely tunable ultrafast single-soliton MIR laser sources, and this method can facilitate the design of other SSFS-based laser systems for single-soliton generation.