The steady-state solutions for higher harmonic gratings that describe the space-charge field in photorefractive materials are derived without restrictions within the shallow trap model. The analysis emphasizes that the amplitudes of the higher harmonic gratings appear strongly for increasing values of both the modulation depth and the grating spacing, and for decreasing values of the external static field as in the Kukhtarev single-species model. However, unlike this early model, the harmonic field amplitudes increase as the average excitation intensity increases. The efficient accumulation of charge carriers in the shallow traps,. due to high density and low thermal excitation rate of shallow centers, also enhances the amplitudes of higher harmonic gratings.