A prototype Emission-Transmission Computed Tomography (ETCT) system is being developed that will acquire single-slice x-ray transmission CT images simultaneously with single photon emission computed tomography (SPECT) images. This system will permit the correlation of anatomical information from x-ray CT with functional information from SPECT images. The patient-specific attenuation map derived from the x-ray CT images can be used to perform attenuation correction of the SPECT images, so that accurate quantitative information can be obtained. The fan-beam scanning geometry and the use of a segmented HPGe detector array impose special constraints on the design of the collimator for the system. Based on a signal detection model, an efficiency-resolution figure of merit (ERFM) as a function of the collimator geometric efficiency, system resolution width, and object diameter is defined. The ERFM is proportional to the square of the detection signal-to-noise ratio. The collimator design parameters can then be optimized by optimizing the ERFM for an anticipated object diameter. The collimator point-spread function, geometric efficiency, and resolution are calculated. The collimator optimized for the detection of a 1-cm object will have a single-slice point source efficiency of 1.2 X 10(-4), and a FWHM of 6.5 mm at the center of the reconstruction circle, at 12 cm from the collimator face. The minimum object contrast which will give a detection SNR of 5 is 74%, for a total accumulated count per slice of 2 X 10(6).