Line-commutated rectifiers (LCRs) are widely used in various industrial applications, wherein they are also known to be a significant source of harmonics. The dynamic phasor (DP) modeling approaches have been well studied in the literature to simulate the dynamics of power systems and their components including harmonics. In this paper, the state-of-the-art analytical DP (ADP) models of LCRs, which relate the ac and dc subsystems through complicated switch functions, are first investigated. Then, a new parametric DP (PDP) model of LCRs is proposed, wherein the DP dynamics of rectifier/dc-link are represented using a set of explicit algebraic functions that are numerically established. Rigorous computer studies demonstrate that the proposed PDP methodology is capable of accurately predicting the steady-state and transient responses of LCR systems under a wide range of loading conditions, while providing significant computational advantages over the conventional detailed model and the established ADP models.