The deposition of an overlay of higher refractive index than the cladding in a Long Period Fiber Grating (LPFG) permits to improve the sensitivity to ambient refractive index changes in a great manner. When the overlay is thick enough, one of the cladding modes is guided by the overlay. This causes important shifts in the effective index values of the cladding modes, and henceforward fast shifts of the resonance wavelength of the attenuations bands in the transmission spectrum. This could be applied for improving the sensitivity of LPFG sensors. The problem is analysed with a numerical method based on LP mode approximation and coupled mode theory, which agrees with so far published experimental results.