The Computed Tomography Imaging Spectrometer (CTIS) is a snapshot hyperspectral camera based on computational imaging. Typical designs use a Keplerian beam expander to limit the imaged scene and decrease the incident ray angles. We have found that the use of a Galilean beam expander instead can be beneficial. Often a smaller system with a better optical quality is achievable with the disadvantage of a vignetted image. Results of a comparison between both designs based on a prototype will be shown. Furthermore, we present our miniaturized CTIS system, which uses the Galilean design.