We measured the size and temperature dependence of the optical nonlinear cross section (σeff), the carrier recombination time (τ), and the dephasing time T2 using CdS0.12Se0.8 microcrystallites embedded in alkaline multicomponent glasses and CdSe microcrystallites embedded in SiO2 thin film using the folded-boxcar configuration of degenerate-four-wave-mixing. As the average radius of a CdS0.12Se0.8 microcrystallite decreased from 10 to 1 nm, the values of σeff and the carrier recombination time changed from 2.6x10-16 to 1.1x10-16 cm2 and from 70 to 2 psec, respectively. The smaller a microcrystallite was, the faster the carrier recombination time became. The size dependence of the carrier recombination time showed that an energy level structure of microcrystallites with a radius of less than a few nanometers is a two-level system, for which it was theoretically known that σeff was proportional to T2. The size and temperature dependence of T2 for the CdS0.12Se0.8 microcrystallites revealed the presence of the acoustic-phononassisted relaxation processes different from the pure-dephasing processes in the dephasing processes. The dependency indicated that longer T2 might enhance σeff. We investigated the enhancement for a nonlinear cross section in CdSe microcrystallites embedded in SiO2 thin film by becoming longer T2. The carrier recombination time, σeff, and T2 of the 3-nm-average-radius CdSe microcrystallites embedded in a SiO2 thin film were 40 psec, 4.5x10-15 cm2, and 150 fsec. The σeff was ten times as large as σeff for the 3-nm-average-radius CdS0.12Se0.88 microcrystallites embedded in alkaline multi-component glasses. The T2 was ten times as long as the extrapolated value for the same size CdS0.12Se0.88 microcrystallites doped in the glasses. We conclude that the longer T2, originated from the changing of the surface and interface, enables the enhancement.