The usage of pinholes is very important in preclinical micro-SPECT. Pinholes can magnify the object onto the detector, resulting in better system resolutions than the detector resolution. The loss in sensitivity is usually countered by adding more pinholes, each projecting onto a specific part of the detector. As a result, gamma rays have an oblique incidence to the detector. This causes displacement and increased uncertainty in the position of the interaction of the gamma ray in the detector, also known as parallax errors or depth-of-interaction (DOI) errors. This in turn has a large influence on image reconstruction algorithms using ray tracers as a forward projector model, as the end-point of each ray on the detector has to be accurately known. In this work, we used GATE to simulate the FLEX Triumph-I system (Gamma Medica-Ideas, Northridge, CA), a CZT-based multi-pinhole micro-SPECT system. This system uses 5 mm thick CZT pixels, with 1.5 mm pixel pitch. The simulated information was then used to enhance the image resolution by accurately modeling the DOI. Two hundred point sources were simulated and rebinned to use the DOI information. This data was then used in a GPU-based iterative reconstruction algorithm taking the simulated DOI into account. The average displacement was then determined for all point sources, and the FWHM was calculated in three dimensions, by fitting the point sources with 3D Gaussians. We show that the displacement is reduced by 83% on average. We also show a 15% resolution gain when only 5 DOI levels are used.