We have measured the thermal conductance,G,of≈1&mgr;m thick low stress silicon nitride membranes over the temperature range,0.06<T<6K, as a function of surface condition. ForT>4K,Gis independent of surface condition indicating that the thermal transport is determined by bulk scattering. ForT<4K, scattering from membrane surfaces becomes significant. Membranes which have submicron sized Ag particles glued to the surface or are micromachined into narrow strips have aGthat is reduced by a factor as large as 5 compared with that of clean, solid membranes with the same ratio of cross section to length. ©1998 American Institute of Physics.