There is an apparent conflict between the configurational entropy theory-based inference that an equilibrium liquid's heat capacity, C-p,(liq), decreases abruptly to the C-p of the crystal phase at a temperature T-2 and the recent conclusion that C-p,(liq), may decrease continuously to zero at 0 K [J. Chem. Phys. 2000, 113, 751]. An examination of this inference here shows that the theory itself had neither supported the Kauzmann entropy extrapolation nor suggested an abrupt C, decrease at a temperature above 0 K. On the basis of geometrical construction of the entropy plots for a P-type liquid, o-terphenyl, it is argued that the size of the cooperatively rearranging region may not diverge at T2 and that a Liquid's configurational entropy cannot be proportional to its excess entropy. The experimentally-determined non-Arrhenius variation of viscosity over a relatively narrow T-range can be reconciled with the S-conf variation without requiring that there be an underlying thermodynamic transition at T > 0 K. Thus the original configurational entropy theory does seem compatible with the continuous decrease of C-p and S-conf of an equilibrium liquid to zero values at 0 K.