We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating these convolution operations as they are typically the most expensive part of the computation. We follow two approaches: First, for some practically important specific point-spread functions, algorithmically efficient sliding window or list processing techniques can be used. In some constellations this allows faster computation than via the Fourier domain. Second, as iterations progress, computation of convolutions can be restricted to subsets of pixels. For moderate thinning rates this can be done with almost no impact on the reconstruction quality. Both approaches are demonstrated in the context of Richardson-Lucy deconvolution but are not restricted to this method.