The two-phase thermodynamic (2PT) model [S.-T. Lin et al., J. Chem. Phys. 119, 11792-11805 (2003)] provides a promising paradigm to efficiently determine the ionic entropies of liquids from molecular dynamics. In this model, the vibrational density of states (VDoS) of a liquid is decomposed into a diffusive gas-like component and a vibrational solid-like component. By treating the diffusive component as hard sphere (HS) gas and the vibrational component as harmonic oscillators, the ionic entropy of the liquid is determined. Here we examine three issues crucial for practical implementations of the 2PT model: (i) the mismatch between the VDoS of the liquid system and that of the HS gas; (ii) the excess entropy of the HS gas; (iii) the partition of the gas-like and solid-like components. Some of these issues have not been addressed before, yet they profoundly change the entropy predicted from the model. Based on these findings, a revised 2PT formalism is proposed and successfully tested in systems with Lennard-Jones potentials as well as many-atom potentials of liquid metals. Aside from being capable of performing quick entropy estimations for a wide range of systems, the formalism also supports fine-tuning to accurately determine entropies at specific thermal states.