Digital carrier phase estimation (CPE) is used in coherent optical receiver to estimate and track carrier phase. The carrier phase estimated from a single symbol is corrupted by noise; hence, it is necessary for CPE to average a block of symbols to mitigate the noise effect. Symbols with significant noise in the averaging block can severely distort the overall phase estimation, especially when the averaging block is small. We propose a selective averaging (SA) method to identify those symbols with significantly large noise and exclude them in the phase averaging process of CPE. We apply our proposed SA technique to the decision-aided maximum likelihood (DAML) CPE and demonstrate via Monte Carlo simulation and experimental results that the modified DA-ML has better optical signal-to-noise ratio (OSNR) performance compared to the conventional DAML in large laser linewidth and medium to high OSNR region.