A new method for measuring the interface fracture energy Gamma(i) for thin metal films on dielectrics has been used to study the interface between vapor deposited Cu films and various dielectric substrates (SiO2, SiNx and polyimide). For fixed Cu film thickness, the ordering of Gamma(i) from lowest to highest has been established as : Cu/SiNx --> Cu/SiO2 --> Cu/polyimide. For a given interface, the effects on Gamma(i) of Cu layer thickness have been found to be small for thin films in the range 50-500 nm. Gamma(i) increases slightly with layer thickness. There are also small effects on Gamma(i) of mode mixity angle, psi : Gamma(i) increases as psi increases from similar to 0 to similar to 50 degrees.