We present a low-complexity carrier estimator with an effective filter length that automatically adapts according to the signal-to-noise ratio, laser-linewidth-symbol-duration product, nonlinear phase noise, and modulation format. Laser-linewidth and frequency-offset tolerances are studied. The filter length of a carrier estimator is shown to affect the cycle slip probability besides the bit-error rate (BER) performance. Considering that forward-error-correction codes are not robust to burst errors and phase slips, we demonstrate that filter-length optimization is necessary to avoid spectral-efficiency reduction in pilot assisted systems and potential system failures in differential encoding systems. Our estimator achieves a lower cycle slip probability and a greater nonlinear phase noise tolerance than DiffFE-MPE, DiffFE-BPS, and complex-weighted decision-aided maximum-likelihood (CW-DA-ML) estimator. DiffFE-MPE and DiffFE-BPS refer to the differential frequency estimator (DiffFE) followed by block Mth power phase estimator (MPE) and blind phase search (BPS), respectively. For a 4100 km quaternary phase-shift keying transmission at a BER of 2.5 x 10(-2), our estimator achieves a cycle slip probability of 2.9 x 10(-7) compared to 5.6 x 10(-6), 5.3 x 10(-6), and 3.2 x 10(-7) for DiffFE-MPE, DiffFE-BPS, and CW-DA-ML, respectively.