We have developed three improved heat transfer models, which allow prediction of the thermal conductivity of evacuated and gas-filled fibrous insulations. These models take into account the coupling between the solid conduction of the fibre system and the gaseous conduction of the gas in the pore space. They use cell configurations, in which the contact resistance between two neighbouring fibres can be modelled by statistical considerations. Results from the derived models are compared with data obtained for 15 different fibre insulations, which have been investigated in evacuable, load-controlled guarded hot plate systems. Experimentally changed parameters were gas pressure, temperature and density of specimens.