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We report on a single-frequency fiber master oscillator power amplifier utilizing a polarization-maintaining step-index fiber with an Al/Ce/F core-glass composition doped with a very high Yb concentration (0.25 at.%). This design made it possible to use a very short fiber (~1 m) and to coil it in a tight radius (4 cm in the amplifier, while 2 cm gave similarly negligible bending loss) so that the packaged system is one of the most compact reported to date (~0.6 L). The use of a short fiber increased the threshold for stimulated Brillouin scattering well above 100 W while maintaining near-ideal beam quality. The fiber was pumped with a diode-pumped solid-state laser and cooled passively by spooling it on a grooved aluminum mandrel. The amplifier produced a strongly linearly polarized output at 1064 nm in the fundamental mode (<i>M²</i> ≤ 1.2) with a 150 kHz linewidth and a power of 81.5 W for 107 W of launched pump power. No deleterious effects from the elevated thermal load were observed. The residual photodarkening loss resulting from the high Yb concentration, found to be small (~0.7 dB/m inferred at 1064 nm) with accelerated aging, reduced the output power by only ~20% after 150 h of operation.