The combination of in situ stress measurements, low-energy electron diffraction, and scanning tunneling microscopy reveals the intimate relation between film structure and film stress for epitaxial growth of Ni on W(110) in the monolayer range. In contradiction to lattice mismatch considerations, we measure tremendous compressive stress in the pseudomorphic Ni film, where tensile film stress is expected from strain arguments. Surface stress of the film-substrate composite is proposed to be much more relevant for the description of film stress in the submonolayer range than lattice mismatch arguments are.