In micro-SPECT imaging, it can be challenging to model accurately the peripheral regions of a pinhole's response function, which correspond to large photon angles of incidence on the pinhole aperture. While it is possible, in principle, to simulate pinhole penetration and scatter accurately, uncertainties in the exact shape of the manufactured pinhole profile, or in detector sag angles during a SPECT orbit are problematic, especially for multi-pinhole systems where inconsistencies among projections can cause high-contrast streak artifacts in reconstructed images. We developed a method to reduce such artifacts, and tested it with data acquired on the Harvard Medical School μSPECT scanner. In this approach, we pre-calculate a set of rolled-off two-dimensional projection masks, one for each detector at each gantry angular position; during iterative reconstruction, the estimated and measured projections are both multiplied by the appropriate mask, which greatly reduces the magnitude of inconsistencies near the axial extrema of the pinhole projections. To compute the masks, we simulate by ray-tracing two sets of projection data from a uniform cylindrical emitter that fills the reconstruction field-of-view. The first set is simulated using the nominal pinhole maximum opening angle (73.6 degrees for our system); the second assumes the same opening angle, but the probability of each ray-traced photon path is weighted by a Hanning-window factor which decreases smoothly from unity (for all paths with angles of incidence within an opening angle less than 53.6-deg) to zero at 73.6-deg. The masks are then calculated by dividing the second set of simulated projections by the first. When this method was used to reconstruct measured high-count projections from Tc-99m phantoms, the streak artifacts were greatly reduced with no apparent loss of axial spatial resolution. Weighted reconstruction of Hanning-windowed projections is an effective approach for artifact reduction in μSPECT imaging.