We report on a passively mode-locked all-fiber laser oscillator at $1.5\mu \mathrm{m}$ based on heavily doped phosphate-glass active fiber. An active fiber only $20\mathrm{cm}$ long is sufficient to produce as much as $2.4\text{\hspace{0.17em} W}$ of average output power directly from the oscillator. The width of the mode-locked pulses varies from $8\mathrm{ps}$ at the lowest output power in the mode-locked state to $44\mathrm{ps}$ at the highest power. Our picosecond laser oscillator features a high repetition rate of $95\mathrm{MHz}$ and high peak pulse power of $\sim 540\mathrm{W}$ . The oscillator combines the convenience of all-fiber construction with power performance that was previously achievable only with mode-locked bulk-optic laser oscillators or more complex systems involving fiber amplifiers.