In this work, we introduce an improved prototype of the imaging system that combines three-dimensional optoacoustic tomography (3D-OAT) and laser ultrasound tomography slicer (2D-LUT) to obtain coregistered maps of tissue optical absorption and speed of sound (SOS). The imaging scan is performed by a 360 degree rotation of a phantom/mouse with respect to a static arc-shaped array of ultrasonic transducers. A Q-switched laser system is used to establish optoacoustic illumination pattern appropriate for deep tissue imaging with a tunable (730-840 nm) output wavelengths operated at 10 Hz pulse repetition rate. For the LUT slicer scans, the array is pivoted by 90 degrees with respect to the central transducers providing accurate registration of optoacoustic and SOS maps, the latter being reconstructed using waveform inversion with source encoding (WISE) technique. The coregistered OAT-LUT modality is validated by imaging a phantom and a live mouse. SOS maps acquired in the imaging system can be employed by an iterative optoacoustic reconstruction algorithm capable of compensating for acoustic wavefield aberrations. The most promising applications of the imaging system include 3D angiography, cancer research, and longitudinal studies of biological distributions of optoacoustic contrast agents (carbon nanotubes, metal plasmonic nanoparticles, fluorophores, etc.).