Image deblurring is essential to high resolution imaging and is therefore widely used in astronomy, microscopy or com- putational photography. While shift-invariant blur is modeled by convolution and leads to fast FFT-based algorithms, shift- variant blurring requires models both accurate and fast. When the point spread function (PSF) varies smoothly across the field, these two opposite objectives can be reached by inter- polating from a grid of PSF samples. Several models for smoothly varying PSF co-exist in the literature. We advocate that one of them is both physically- grounded and fast. Moreover, we show that the approximation can be largely improved by tuning the PSF samples and inter- polation weights with respect to a given continuous model. This improvement comes without increasing the computa- tional cost of the blurring operator. We illustrate the developed blurring model on a deconvo- lution application in astronomy. Regularized reconstruction with our model leads to large improvements over existing re- sults.