Harmonically mode-locked Er-fiber soliton lasers have become a reliable source of high-repetition-rate picosecond pulses in high-speed communications and photonic analog-to-digital conversion systems because of their low-noise, dropout-free operation. We have fabricated such a laser with a strongly dispersion-managed cavity and modeled its operation, and we have found that dispersion management significantly extends the power range over which uninterrupted single-pulse production is attained and dramatically decreases the effects of amplified spontaneous emission on the phase noise of the laser.