Nonuniform, non-Cartesian k-space trajectories enable fast scanning with reduced motion and flow artifacts. In such cases, the data are usually convolved with a kernel and resampled onto a Cartesian grid before reconstruction. For trajectories such as undersampled variable-density spirals, the mainlobe width of the kernel for undersampled high spatial frequencies has to be larger to limit the amount of aliasing energy. Continuously varying the kernel extent is time consuming. By dividing k-space into several annuli and using appropriate mainlobe widths for each, the aliasing energy and noise can be reduced at the expense of lower resolution towards the edge of the field of view (FOV). Resolution can instead be preserved at the center of the FOV, which is expected to be free of artifacts, without any artifact reduction. The image reconstructed from each annulus can be deapodized separately. The method can be applied to most k-space trajectories used in MRI. 2007 Wiley-Liss, Inc