SPECT acquisition parameters can be optimized using the Ideal Observer (IO) applied to projections. The IO implicitly has perfect knowledge of the image formation process, and thus its performance reflects the best achievable with perfect compensation. However, SPECT images are often reconstructed with imperfect or no compensation. This mismatch between the reconstruction and IO can give rise to suboptimal performance when human observers interpret SPECT images. In this study, we investigated the importance of including 'model mismatch' (MM) in the IO in the context of myocardial perfusion SPECT for a signal known exactly/background known statistically (SKE/BKS) task. We optimized the energy window using the IO with and without MM. We evaluated IO performance when the observer had (1) a perfect and (2) no or (3) an approximate model of scatter. We used an anthropomorphic model observer (AO) as a benchmark for human observer performance and compared optimal energy windows. IO performance was relatively insensitive to energy window settings for case 1. Performance for case 2 was significantly worse than for 1, and the optimal window width was 13-15%. For case 3, performance was similar to case 1. Performance for the AO was similar to cases 2 and 3 when scatter compensation was or was not, respectively, included in the reconstruction. Incorporating MM into the IO is a new approach for improving agreement of the IO with human observers. This allows optimization of acquisition and instrumentation parameters in the presence of non-ideal compensation methods more efficiently than reconstructed-image-domain AOs.