We report a Raman scattering study of low-temperature, pressure-induced melting of the charge-density-wave (CDW) phase of 1T-TiSe2. Our measurements reveal that the collapse of the CDW state occurs in three stages: (i) For P<5 kbar, the pressure dependence of the CDW amplitude mode energies and intensities are indicative of a "crystalline" CDW regime; (ii) for 5<P<25 kbar, there is a decrease in the CDW amplitude mode energies and intensities with increasing pressure that suggests a regime in which the CDW softens, and exhibits enhanced fluctuations; and (iii) for P>25 kbar, the absence of amplitude modes reveals a metallic regime in which the CDW has melted.