We consider the problem of deblurring images which have been blurred by different reasons during image acquisition. We propose a variational approach admitting spatially variant and irregularly shaped point-spread functions. By involving robust data terms, it achieves a high robustness particularly with respect to imprecisions in the estimation of the point-spread function. A good restoration of image features is ensured by using non-convex regularisers and a strategy of reducing the regularisation weight. Experiments with irregular spatially invariant as well as with spatially variant point-spread functions demonstrate the good quality of the method as well as its stability under noise.