Flow of non-Newtonian fluids in rough-walled rock fractures is common in many technological processes in oil and gas industry. A numerical study of power-law fluid flow in rough-walled fractures is carried out under the assumptions of the lubrication theory approximation. It is shown that, in a self-affine fracture, varying the exponent of the power-law fluid may lead to a redirection of flow compared to a Newtonian fluid flow field. This effect is observed even though the fracture landscape is isotropic, i.e. no preferential flow paths have been created in the model by e.g. relative displacement of the fracture faces. In another fracture, one that contains an obstacle represented by a spot of zero aperture, the spread of the flow around the obstacle is again controlled by the power exponent of the fluid. The fluid being more shear-thinning leads to a channelization of the flow in such a fracture. "Channelization" here refers to the fluid velocity component in the direction of the applied pressure gradient becoming larger as compared to the velocity component in the direction normal to the overall flow direction as the fluid becomes more shear-thinning. A channelization is also observed in a fracture containing a local zone of an elevated aperture. The effects of rheology on the spread and redirection of flow in a fracture of variable aperture are crucial for optimization of transport and placement of particles or tracers in natural and man-made fractures. (C) 2013 Elsevier Ltd. All rights reserved.