Accurate computation of ice-stream location and dynamics is a key aspiration for theoretical glaciology. Ice-sheet models with thermo-viscous coupling have been shown to exhibit stream-like instabilities using shallow-ice approximation mechanics, but the location and width of these streams depends on the numerical implementation and are not unique. We present results from thermo-viscously coupled ice-sheet models incorporating membrane stresses. Spontaneous generation of fast-flowing linear features still occurs under certain parameter regimes, with computed stream widths between 20 km to 100 km, comparable with observations. These features are maintained as the grid-size is decreased. The thermo-viscous feedback mechanism that generates ice-streams under the shallow ice approximation still operates, now selecting a unique stream size. Computations of thermo-viscous ice flows should include membrane stresses when the bed is approximately flat, e.g. parts of Antarctica and former ice-sheets of the Northern hemisphere. Previous calculations of spontaneous ice-stream generation using the shallow ice approximation should be reassessed.