Two-dimensional elliptic water-wave models based on the mild-slope equation find wide application in engineering and other studies. Model results are often adversely influenced by approximate treatment of the open boundary condition. A method to incorporate the exact radiation condition at infinity in finite-difference models is therefore developed. Since directly matching the solutions within the computational domain to those outside is too stringent a requirement, the new method is based on minimizing the overall discrepancy between the solutions along the open boundary. This relaxation permits the development of a suitable solution method, which is tested against analytical solutions for two situations. Satisfactory results are obtained with no artificial reflection of wave energy from the open boundary, even when it is placed very close to the scatterer.