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Inside a femtosecond laser oscillator, no coupling mechanism between the propagation speeds of the carrier and the pulse envelope exists. Therefore, the relative delay between carrier and envelope of a femtosecond oscillator will exhibit irregular fluctuations unless this jitter is actively suppressed. Both intensity and beam pointing fluctuations in the laser can introduce carrier-envelope phase changes. Based on our analysis, we are capable of reducing or avoiding certain mechanisms by proper design of the laser cavity. We use such an optimized cavity to stabilize the carrier envelope-phase to an external reference oscillator with a long-term residual jitter corresponding to only 10 attoseconds in a (100 kHz-0.01 Hz) bandwidth. This is the smallest long-term timing jitter of a femtosecond laser oscillator demonstrated to date. However, it is important to note that this stabilization was obtained with an f-to-2f heterodyne technique using additional external spectral broadening in a microstructure fiber which introduces additional carrier-envelope phase noise. We present a direct heterodyne measurement of this additional carrier-envelope phase noise due to the continuum generation process.