The bit-error-rate performance of a multilevel phase-shift-keying (PSK) signal can be easily degraded by a slight phase distortion induced by the setting errors of the modulator such as the offsets of bias voltages. To solve this problem, we examine the possibility of using the data-aided phase noise estimation (DAPNE) algorithm, which has been originally proposed for the reduction of differential phase noise. The experimental results show that DAPNE can enhance the tolerance to the setting errors of differential quadrature PSK and 8-ary PSK modulators.