Factors influencing the design of full coverage drilled plate wall cooling systems for gas turbine combustors are studied. It is shown that the large number of small diameter holes required result in a low Reynolds number operating regime. The physical features giving rise to the hole pressure loss are examined, and it is shown that under hot conditions heat transfer within the hole can appreciably alter the hole mass flow for a fixed pressure loss. It is shown that this effect may be used to estimate the hole outlet temperature and the results show that the heat transfer within the combustor wall may be very significant. The rise in coolant temperature within the wall appreciably alters the blowing rate and hence influences the hot gas side convective heat transfer to the plate. The influence of an impingement plate on hole discharge coefficients is also investigated and shown to be small.