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The 'soft glassy rheology' (SGR) model gives an appealing account of the flow of non-ergodic soft materials in terms of the local yield dynamics of mesoscopic elements. Newtonian, power-law, and yield-stress fluid regimes arise on varying a 'noise temperature', x. Here we extend the model, to capture the idea that the noise is largely caused by yield itself. The extended model can account for the viscosity-bifurcation and shear-banding effects reported recently in a wide range of soft materials. A variant model may shed light on shear banding and strain-rate hysteresis seen in glassy star polymer solutions.