Charge transfer near the threshold of polymer film transition (induced by a low uniaxial pressure) to the high-conductivity state is studied in an attempt to tackle the question of how the energy band structure of a wide-gap organic insulator varies near this threshold. The I-V characteristics of poly(diphenylenephthalide) films of various thickness versus uniaxial pressure are analyzed. The results obtained are treated within the model of space-charge-limited injection currents. The parameters of the injection model, such as the equilibrium concentration of electrons, electron mobility, the occupation of traps, etc., are estimated. It is concluded that deep traps due to an excess charge may appear in the energy gap of the polymer near the imref. This probably causes a narrow subband to arise, and charge transfer via this subband increases the charge carrier mobility and, hence, conductivity.