Spatially-adaptive intensity bounds on the image estimate are shown to be an effective means of regularising the ill-posed image restoration problem. For blind restoration, the local intensity constraints also help to further define the solution, thereby reducing the number of multiple solutions and local minima. The bounds are defined in terms of the local statistics of the image estimate and a control parameter which determines the scale of the bounds. Guidelines for choosing this parameter are developed in the context of classical (nonblind) image restoration. The intensity bounds are applied by means of the gradient projection method, and conditions for convergence are derived when the bounds are refined using the current image estimate. Based on this method, a new alternating constrained minimisation approach is proposed for blind image restoration. On the basis of the experimental results provided, it is found that local intensity bounds offer a simple, flexible method of constraining both the nonblind and blind restoration problems.