We have theoretically studied and quantitatively analysed the enhancement of the thermal conductivity of AlN microceramics (i.e. commercially available powder) by the insertion of AlN nanosized particles of high-specific surface area, and of Y(2)O(3) and CaO as sintering additives. We have also studied the enhancement of the thermal conductivity of AlN nanoceramics by using Y(2)O(3) as the sintering additive. Thermal conductivity calculations have been carried out by applying the Callaway theory in its full form and by incorporating a detailed and accurate account of three-phonon processes. The role of densification of the AlN ceramic samples in enhancing the thermal conductivity has been quantified at low, intermediate and high temperatures. In addition to explaining the experimentally observed room-temperature conductivity results, the conductivity variation has been predicted over a large temperature range.