An already-connected telephone call is conferenced in a seamless manner that is transparent to the call participants, after which one or more additional participants may join the conference. The existing call is preferably moved to a conference bridge responsive to an existing call participant either logging on to a network-accessible user interface (such as a web page or portal-type page) or entering some special key or key combination using the participant's phone (which may be a software application that provides phone-like services). The participant requesting the move may be authenticated, and the authorization of the participant to request the move may be verified, before moving the call.