Low-dose X-ray computed tomography (CT) is a major area of research due to the diagnostic capability of CT counterbalanced by the risk of radiation exposure. The standard method for reducing the dose is to decrease the tube current, but this negatively impacts image quality at high dose reduction factors due to photon starvation effects. We investigate an alternative paradigm, called SparseCT, in which a multi-slit collimator (MSC) is placed between the source and the patient. Interrupting the X-ray beam in this way reduces radiation dose to the patient and produces undersampled data from which the image can be estimated using sparse image reconstruction techniques. However, the MSC introduces a number of new considerations, including penumbra effects that require wider slits and more spacing between slits in order to optimize dose efficiency and beam separation. These design choices reduce incoherence in the undersampling scheme and affect the performance of standard edge-preserving/sparsity-promoting regularizers. Here, we simulate these effects in the ideal setting where penumbra effects do not increase the noise in the sinogram. For modest 4-fold retrospective undersampling factors, we observe a slight degradation in an abdominal scan between incoherent-optimal and practical MSC designs for SparseCT. In the future, we plan to use the simulation to inform MSC design prior to fabrication.