Subspace-based parameter estimators, like HTLS in nuclear magnetic resonance spectroscopy, are efficient and accurate in estimating parameters of a sum of exponentially damped sinusoids. But they suffer from a serious drawback that little prior knowledge can be incorporated which is important for the resolution and accuracy. Recently, one type of prior knowledge, known frequency and damping of some exponentials, has been successfully incorporated into HTLS. In this paper, another type of prior knowledge, known frequency and phase of some exponentials, is incorporated into HTLS. In addition, some variants are derived which allow some combinations of prior knowledge of frequency, damping and phase. The benefit of the new extended HTLS methods is confirmed via a simulation study. The same ideas can be used directly in other subspace-based parameter estimation methods as well.