Generation of two-photon wavepackets, produced by spontaneous parametric down conversion in crystals with linearly chirped quasi-phase matching grating, is analyzed. Although being spectrally broad, two-photon wavepackets produced this way are not Fourier transform limited. In the paper we discuss the temporal compression of the wavepackets, exploiting the insertion of a standard optical fiber in the path of one of the two photons. The effect is analyzed by means of full numerical calculation and the exact dispersion dependencies in both the crystal and the fiber are considered. The study opens the way to the practical realization of this idea.