We describe the surface structures following submonolayer Cu deposition on Si͑001͒ and subsequent hydrogen termination as characterized by scanning tunneling microscopy. Cu adsorption at 870 K results in a characteristic ͑2 ϫ 8͒ island+ vacancy structure, as previously reported. In addition, occasional structures are observed attributed to Cu in surface interstitial sites. After H termination, the dominant features of the island+ vacancy structure remain, but the size and distribution of the structures are significantly altered. Based on the atomic-scale appearance of both the clean and H-terminated structures, we propose that within the ͑2 ϫ 8͒ island+ vacancy structure all surface atoms are Si, with all Cu subsurface, contrary to previous structural models.