Connection graph resolution (cg-resolution) was introduced by Kowalski as a means of restricting the search space of resolution. Several researchers expected unrestricted connection graph (cg) resolution to be strongly complete until Eisinger proved that it was not. In this paper, ordered resolution is shown to be a special case of cg-resolution, and that relationship is used to prove that ordered cg-resolution is strongly complete. On the other hand, ordered resolution provides little insight about completeness of first order cg-resolution and little about the establishment of strong completeness from completeness. A first order version of Eisinger’s cyclic example is presented, illustrating the difficulties with first order cg resolution. But resolution with selection functions does yield a simple proof of strong cg-completeness for the unit-refutable class.