Results of simulations and experiments on a high-power double-pass explosively pumped photo-dissociation iodine laser (EPDL) with phase conjugation (PC) are presented. The laser system consists of a master oscillator, two exploding amplifiers with a working mixture 25 Torr C3F7I+125 Torr Xe and amplifier aperture of 15 cm, and an SBS-mirror. The SBS mirror consists of an angular selector of Stokes radiation, an ordered raster of small diffraction lenses, a main focusing lens, and an SBS cell. The calculation model and the computer code package take into account the actual three-dimensionality of space, transient effects at SBS, parasitic reflections of laser radiation from elements of the optical scheme, intrinsic amplified spontaneous emission of amplifiers, radiation losses in the optical path, non-uniformity of gain, and radiation refraction on optical non-uniformities of the active medium caused by a shock wave. In the laser system, an optimal configuration of the SBS mirror is used. It possesses unique properties if compared to the existing specimens of SBS mirrors. It stably gives a nearly ideal quality of PC at any level of SBS saturation, i.e. any reflection coefficient that has been confirmed by experimental laboratory investigations. As a result of investigations, a good agreement of calculated results with available experimental data has been demonstrated in energy, time dependence of power and Strehl number of output radiation. The considered EPDL has output energy of about 400 J and brightness of about 1012 J/sr. It has been found that with the increase of the flux density of an input signal from the master oscillator in the range 0.01-20 W/cm2 the brightness of EPDL output radiation increases as well whereas the full energy varies relatively slightly. It has been shown that parasitic reflections of laser radiation from the ends of amplifiers and elements of the optical scheme with a coefficient exceeding 10-7 considerably decrease the axial brightness of output radiation. In order to reduce the harmful effect of parasitic reflections on brightness the distance between amplifiers should be increased.