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In the soliton laser, feedback from a pulse-shaping fiber enables the production of ultrafast pulses of controlled shape and width. Successful operation, however, requires maintenance of the correct optical phase of this feedback. We describe a simple but effective servo control that locks to the required phase, while simultaneously stabilizing output power. We also show that the stabilized soliton laser action involves passive mode-locking. Finally, we describe experiments that reveal, in considerable detail, how the pulse shaping takes place. In particular, our experiments show that closure is not required separately of the laser's two coupled cavities.