For the enhancement of single-channel speech corrupted by acoustic noise, recently short-time Fourier transform domain clean speech estimators were proposed that incorporate prior information about the clean speech spectral phase. Instrumental measures predict quality improvements for the phase-aware estimators over their conventional phase-blind counterparts. In this letter, these predictions are verified by means of listening experiments. The phase-aware amplitude estimator on average achieves a stronger noise reduction and is significantly preferred over its phase-blind counterpart in a pairwise comparison even if the clean spectral phase is estimated blindly on the noisy signal.