We show that the infrared edge of supercontinua generated in solid core photonic bandgap fibers is characterized by a very different temporal behavior than the one obtained in standard fibers. In particular, pulse-to-pulse spectral power fluctuations are significantly reduced near the bandgap edge, and the statistical distribution is quasi-gaussian. The spectral dynamics of this process and statistical properties are investigated experimentally and confirmed by numerical simulations. The reduction of power fluctuations originates from the cancellation of the soliton self-frequency shift near the bandgap edge.