A theoretical analysis of wave scattering from perfectly reflective random media is developed from general postulates of invariance. Based on only the assumptions of flux conservation and time-reversal invariance, we use random matrix theory to calculate the average reflection coefficients as well as the correlation function between them. As a consequence, enhanced coherent backscattering is obtained. The predicted behavior of the correlations differs substantially from that obtained for the case of semiballistic or diffusive transport.