A simple model for the sintering of materials made of connected fractal aggregates, such as aerogels, is proposed. The densification at small scales is described by an increase of the lower cutoff length accompanied by a decrease of the upper cutoff length, in order to conserve the total mass of the system. General scaling laws are derived which relate the structural characteristics to the mean bulk density. The theory explains quite satisfactorily a large number of experiments on gradually densified silica aerogels.