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We report the usefulness of coarse septa in positron emission tomography (PET) by Monte Carlo simulation. Coarse septa result in higher sensitivity than found with the two-dimensional mode with conventional full septa and lower scatter fraction than the three-dimensional mode without septa. We propose a new scatter correction method using coarse septa, where scatter components are estimated from coincidence data for those line-of-responses that are intercepted by the coarse septa. This scatter correction potentially has the ability to cope with scatter from radioactivity outside the field of view. In addition, we show the feasibility of a lead tungstate PET scanner with coarse septa.