A model for standard line-scan imaging spectrometers with circularly symmetric optics is presented. Using reasonable approximations and special cases to maintain clarity, straight-forward analysis demonstrates design options are constrained due to lack of parameters that can readily be engineered. As a result, compromises must be made. This motivates line-scan imaging spectrometers that utilize anamorphic optics. The presented anamorphic design provides an additional degree of engineering freedom and eliminates the need for compromises required in standard systems. Results from a prototype anamorphic line-scan imaging spectrometer are provided, including Signal-to-Noise Ratios and sample imagery.