Strong E × B plasma flow shear is beneficial for reducing turbulent transport. However, traditional methods of driving flow shear do not scale well to large devices such as future fusion power plants. In this paper, we use a large number of nonlinear gyrokinetic simulations to study a novel approach to increase flow shear: decreasing the momentum diffusivity to make the plasma ‘easier to push’. We first use an idealized circular geometry and find that one can obtain low momentum diffusivity (LMD) at tight aspect ratio, low safety factor, high magnetic shear and low temperature gradient. This is the so-called LMD regime. To drive intrinsic momentum flux, we then tilt the flux surface, making it up–down asymmetric. In the LMD regime, this intrinsic momentum flux drives strong flow shear that can significantly reduce the heat flux and increase the critical temperature gradient. We also consider the actual experimental geometry of the Mega Ampere Spherical Tokamak (MAST) to illustrate that this strategy can be practical and create experimentally significant flow shear. Lastly, a preliminary prediction for the SMall Aspect Ratio Tokamak (SMART) is made.