The behaviour of the pressure exponent in the Sieverts-type empirical law is evaluated for hydrogen permeation through Pd-based membranes under the influence of non-ideal internal diffusion and transport in an asymmetric multilayer porous support. The results show that the non-ideal diffusion causes the pressure exponent to be non-monotone within the temperature range investigated (300-500 degrees C), showing a minimum point indicating the passage from slower internal diffusion to slower transport in support. Additionally, a detailed analysis shows that the maximum transmembrane pressure difference (in terms of maximum feed pressure with constant permeate pressure) is the only operating parameter affecting the uncertainty degree by which the pressure exponent is evaluated. This analysis also shows that the Sieverts-type empirical law can be fully used in the presence of supports. This suggests that an overall transport mechanism resulting from a combination in series/parallel of different elementary mechanisms obeying this law can be also described by the same type of law with a different value of pressure exponent and permeance. Copyright (C) 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.