In two recent papers, C. L. Rino, H. Ngo and V. Kruger (RNK) proposed a novel scheme for tropospheric propagation over one-dimensional (1D) terrain or ocean surfaces. This scheme is based on a boundary integral equation (BIE) formalism, the iterative solution of which is carried out efficiently via the method of ordered multiple interactions (MOMI). An important merit of the RNK scheme is the fact that, being a BIE-based model, it rigorously accounts for the effect of the multiple-scale ocean surface roughness on the propagated field. In their most recent paper, C. L. Rino and V. Kruger suggested that the accelerated version of MOMI proposed by H.-T. Chou and J. T. Johnson (MOMI/CJ) could substantially enhance the efficiency of their scheme. Motivated by this suggestion, this paper proposes a combined RNK/CJ algorithm for propagation over finitely conducting (FC) ocean surfaces. While maintaining its accuracy, the proposed scheme enhances the computational efficiency of the rigorous RNK model by reducing the number of mathematical operations needed in the iterative solution of the governing BIE.