Rotationally resolved vibrational overtone spectra of several CH stretch bands of CF3H have been obtained using a combination of jet-cooling, infrared-optical double-resonance, and infrared laser assisted photofragment spectroscopy detection. The high selectivity and sensitivity of this combination allows measurement of spectral splittings that determine the secondary time scales of vibrational energy redistribution. The spectroscopic results show that in the energy region of the v(CH)=3-5 CH stretch levels, the vibrational energy would remain localized in the mixed CH stretch-bend states on time scales longer than 13-130 ps if coherently excited. This is as much as 2500 times longer than the time scale for energy transfer between the CH stretch and the LICE bend vibrations. Moreover, the results confirm that the energy redistribution dynamics are sensitive to the character of the bath states and not simply to the total vibrational energy.