Large and highly perfect PbSe and PbTe single crystals are grown in closed ampoules by chemical transport via vapour phase in an iodine atmosphere. The growth rates increase by a factor of four and the growth temperature is lowered by 130 K compared to the growth method without iodine as transport agent. Small amounts of silver iodide are used to adjust the iodine vapour pressure at the growth temperature within the closed ampoule by the reaction AgI(s) reversible Ag(s)+I2(g). Steady-state Knudsen cell mass spectrometric analyses reveal the species in the vapour phase predominantly involved in the chemical transport reactions. The reactions responsible for the gain of growth rates are PbTe(s)+I2(g) reversible PbI2(g)+1/2Te2(g), PbSe(s)+I2(g) reversible PbI2(g)+(1/n)SIGMA(n=1)8Se(n)(g), for the PbTe-AgI and the PbSe-AgI chemical vapour transport systems, respectively. At the actual growth temperature T = 970 K the composition of the vapour contains mainly PbI2 and Te2 or PbI2 and Se2 species. The PbI2 vapour pressure depends sensitively on the iodine pressure. The thermal decomposition of AgI adjusts the PbI2 pressure below its saturation vapour pressure and no condensation of PbI2 occurs. The condensation of PbI2 Would inhibit an effective growth process by covering the surface of the growing crystal. The pressure and temperature region for the PbTe-AgI and PbSe-AgI crystal growth systems is calculated.