An eddy-viscosity model is proposed and applied in large-eddy simulation of turbulent shear flows with quite satisfactory results. The model is essentially not more complicated than the Smagorinsky model, but is constructed in such a way that its dissipation is relatively small in transitional and near-wall regions. The model is expressed in first-order derivatives, does not involve explicit filtering, averaging, or clipping procedures, and is rotationally invariant for isotropic filter widths. Because of these highly desirable properties the model seems to be well suited for engineering applications. In order to provide a foundation of the model, an algebraic framework for general three-dimensional flows is introduced. Within this framework several types of flows are proven to have zero energy transfer to subgrid scales. The eddy viscosity is zero in the same cases; the theoretical subgrid dissipation and the eddy viscosity have the same algebraic structure. In addition, the model is based on a fundamental realizability inequality for the theoretical subgrid dissipation. Results are shown for a transitional and turbulent mixing layer at high Reynolds number and a turbulent channel flow. In both cases the present model is found to be more accurate than the smagorinsky model and as good as the standard dynamic model. Unlike the Smagorinsky model, the present model is able to adequately handle not only turbulent but also transitional flow.