Measurements of low-temperature specific heat (1.5-25 K) in glasses of the AgI-Ag2O-B2O3 system reveal that the AgI addition to the borate network enhances the deviations of C p from a T 3 behaviour. An explanation for this is given by considering AgI as responsible for the decreasing coherence of a network where the borate host matrix preserves its local structure. The temperature dependences of C p in the whole explored range are in qualitative agreement with the predictions of the soft-potential model; the specific heat appears to be regulated from extra vibrational states having a nearly fourth-order frequency dependence which tends to become linear with increasing frequency.