We report a new mechanism for intramolecular vibrational redistribution (IVR) in CF3CHFI which couples the CH chromophore vibrations through a strong Fermi resonance to the formal CF stretching normal mode (a heavy atom frame mode) involving the trans F-atom across the CC bond. The analysis is made possible by comparing spectroscopic results with extensive ab initio calculations of the vibrational fundamental and overtone spectra in the range extending to 12 000 cm(-1). Potential energy and electric dipole moment hypersurfaces are calculated ab initio by second order Moller-Plesset perturbation theory (MP2) on a grid involving the CH stretching, two CH bending modes and one high frequency CF stretching normal mode. The potentials are scaled to obtain agreement between the experimental spectrum and the theoretical spectrum calculated by a discrete variable representation technique on this grid. Both spectra are then analyzed in terms of three-dimensional (3D) and four-dimensional (4D) effective vibrational Hamiltonians including Fermi- and Darling-Dennison-type resonances between the CH stretching mode and the CH bending modes and the CF stretching mode. The interaction between the CH modes and the CF mode is clearly visible in the experimental and calculated (4D) spectra. The effective Fermi resonance coupling constants [k(sff)' similar or equal to (40 +/- 10) cm(-1) and k(saf)' similar or equal to (55 +/- 10) cm(-1)] coupling the CH and CF mode subspaces are of about the same magnitude as the intra-CH chromophore Fermi resonances (k(saa)' similar or equal to 56 cm(-1) and k(sbb)' similar or equal to 42 cm(-1), coupling CH stretching mode "s" with the two CH bending modes "a" and "b"). The chiral, pseudo-C-s symmetry breaking coupling (k(sab)' similar or equal to 11 cm(-1)) is complemented by an equally strong coupling through the CF mode (k(sfb)' similar or equal to 15 cm(-1)). It is demonstrated that low order perturbation theoretical analysis using potential constants from a polynomial expansion to represent effective coupling constants gives inadequate results with discrepancies ranging about from factors of 2-5. Time dependent population and wave packet analysis shows essentially complete IVR among the CH chromophore modes within about 100 fs, the 3D and 4D evolutions being similar up to about that time. At longer times of about 250 fs, there is substantial excitation of the CF stretching mode (with initial pure CH stretching excitation). The 4D treatment is then essential for a correct description of the dynamics.