The optimum connection problem for a class of videoconferences in packet-switched networks is studied. The conferees of a particular conference send their images to a chosen node, called the conference center, for processing. The conference center can either send distinct composite video to an individual conferee or multicast the same composite video to all conferees. Depending on how the video is composed, the optimum connection paths form either the minimum conference tree or the minimum conference-multicast tree. Algorithms are designed for finding these trees, and the conference blocking probability in fully connected networks is derived. One to two orders of magnitude reduction of blocking is observed with the use of the optimum connection paths when compared to the strategy which chooses the call-initiating-node as the conference center.