We present new results on single-channel speech separation and suggest a new separation approach to improve the speech quality of separated signals from an observed mix- ture. The key idea is to derive a mixture estimator based on sinusoidal parameters. The proposed estimator is aimed at finding sinusoidal parameters in the form of codevectors from vector quantization (VQ) codebooks pre-trained for speakers that, when combined, best fit the observed mixed signal. The selected codevectors are then used to reconstruct the recovered signals for the speakers in the mixture. Compared to the log- max mixture estimator used in binary masks and the Wiener filtering approach, it is observed that the proposed method achieves an acceptable perceptual speech quality with less cross- talk at different signal-to-signal ratios. Moreover, the method is independent of pitch estimates and reduces the computational complexity of the separation by replacing the short-time Fourier transform (STFT) feature vectors of high dimensionality with sinusoidal feature vectors. We report separation results for the proposed method and compare them with respect to other benchmark methods. The improvements made by applying the proposed method over other methods are confirmed by employing perceptual evaluation of speech quality (PESQ) as an objective measure and a MUSHRA listening test as a subjective evaluation for both speaker-dependent and gender-dependent scenarios.