We analyze the possibility of obtaining a better representation of pure fluid VL coexistence curves by the cubic chain-of-rotators (CCOR) equation of state, which, in the original form, has two temperature dependent parameters, alpha and gamma. Introducing separate gamma parameters for liquid and vapor phases, while retaining the common alpha parameter, has enabled description of saturation pressures and densities of coexisting phases with a high degree of accuracy. As one may expect, this improvement extends also to predictions of superheated vapor densities and subcooled liquid densities at low pressures. However, it has been shown that "tuning" the equation parameters to the saturation curve up to the critical point leads to a thermodynamically inconsistent description of compressed liquid at high pressures as well as to a dramatic increase of enthalpy prediction errors in the critical region. Three common substances, CO2, NH3 and H2O, are taken for illustration.