A hybrid DSMA-CR/CDMA methodology provides efficient access to one of a group of common packet channels in a cell of a spread spectrum wireless communication network. The base station broadcasts status information as to the availability and/or available data rates for each common packet channel (CPCH) or group of CPCH channels. Each mobile station uses the status information to select an available channel and/or a channel with sufficient data rate. The mobile station then starts transmission of a series of access preambles, each of which contains a signature corresponding to the selected channel. The mobile station transmits the preambles at increasing power levels. When the base station detects a preamble transmission, the base station responds with a corresponding acknowledgment. Upon receiving this acknowledgment, the mobile station preferably selects a collision detection (CD) signature and transmits a CD preamble containing that signature. If the base station receives more that one CD preamble, it selects one and responds by sending back a corresponding CD acknowledgement. In response, the mobile station begins to send its packet data along with any closed-loop power control information over the selected CPCH channel. If the MS detects a loss of the downlink channel, the MS halts its CPCH uplink transmission. Also, during a transmission of data, the mobile station that has successfully obtained access can piggy-back data packets one after another so long as it has packets ready to send, up to a maximum limit set by the network.