We describe a Yb-fiber-based laser comb, with a focus on the relationship between the net-cavity dispersion and frequency noise on the comb. While tuning the net-cavity dispersion from anomalous to normal, we measure the relative intensity noise, offset frequency (f(CEO)) linewidth, and the resulting frequency noise spectrum on the f(CEO). We find that the laser operating at zero net-cavity dispersion has many advantages, including an approximately 100× reduction in free-running f(CEO) linewidth and frequency noise power spectral density when compared to the normal-dispersion regime. At the zero-dispersion point, we demonstrate a phase-locked f(CEO) beat with low residual noise.