We developed the first prototype of dual-modality imager combining optoacoustic tomography (OAT) and laser ultrasound tomography (UST) using computer models followed by experimental validation. The system designed for preclinical biomedical research can concurrently yield images depicting both the absorbed optical energy density and acoustic properties (speed of sound) of an object. In our design of the UST imager, we seek to replace conventional electrical generation of ultrasound waves by laser-induced ultrasound (LU). While earlier studies yielded encouraging results [Manohar, et al., Appl. Phys. Lett, 131911, 2007], they were limited to two-dimensional (2D) geometries. In this work, we conduct computer-simulation studies to investigate different designs for the 3D LU UST imager. The number and location of the laser ultrasound emitters, which are constrained to reside on the cylindrical surface opposite to the arc of detectors, are optimized. In addition to the system parameters, an iterative image reconstruction algorithm was optimized. We demonstrate that high quality volumetric maps of the speed of sound can be reconstructed when only 32 emitters and 128 receiving transducers are employed to record time-of-flight data at 360 tomographic view angles. The implications of the proposed system for small animal and breast-cancer imaging are discussed.