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Parallel slat collimators are often employed in hybrid positron emission tomography (PET) to reduce the scatter fraction, decrease singles rates, and create a pseudo 2-D imaging geometry. Similar collimators or inter-slice septa may be used with newer classes of large-area dedicated PET cameras. While conventional parallel slat collimators are adequate for some applications, other collimator designs which produce pseudo 3-D imaging geometries have the potential to greatly improve performance for targeted volume-of-interest (VOI) imaging applications. We have investigated three types of converging slat collimators which may improve shielding of out-of-field-of-view (FOV) photons while greatly increasing sensitivity to the central FOV. Such collimators create a pseudo 3-D imaging geometry and maintain good shielding of scattered events. A series of Monte Carlo simulations were performed for 2-, 3-, 4-, 6-, and 8-head class systems equipped with parallel slat collimators, no collimators (fully 3-D), and the new converging slat designs. Collimator performance was measured in terms of trues sensitivity, singles rejection, scatter fraction, and noise-equivalent counts. The axially-focused slat collimators were found to provide greatly increased sensitivity to the central FOV while also providing better shielding of out-of-FOV events. Whole-body noise equivalent count (NEC) performance for fan slat collimators was nearly identical to that for conventional parallel slat collimators, and VOI NEC was nearly doubled using fan slat collimators. These results suggest that converging slat collimators may provide greatly improved VOI imaging while maintaining good whole-body imaging performance.