A private dialing plan for the communication of packetized voice on a packet-based network using a signaling protocol such as Q.931 to establish, maintain and release switched connections over the network. The dialing plan uses a "telephone number" based on a conventional 10-digit telephone number, such as the user's regular telephone number. A leading single digit consisting of a "0" or a "1" is added in front of the conventional telephone number. A leading "0" indicates that the desired call is to be directed to the called party's on-network computer by means of the Internet, while a leading "1" indicates the call is directed through a special gateway to the called party's conventional telephone.