Collisions between messages simultaneously transmitted by multiple spread-spectrum transmitters are reduced by distributing the transmissions over the available resources of the receiver. The transmitters may be mobile stations and the receiver may be a base station in a CDMA cellular telephone system. Each mobile station uses one or more randomization methods to distribute its transmissions. In the first randomization, the mobile station time- delays its transmissions by a number of chips of the PN code with which it spreads the transmitted signal. A hash function produces the number from an identification number uniquely associated with that mobile station. In a second randomization, the mobile station randomly selects the PN code. In a third randomization, the mobile station inserts a random delay between successive message transmissions or probes if it does not receive an acknowledgement after a predetermined timeout period. A predetermined number of such transmissions is called a probe sequence. In a fourth randomization, the mobile station inserts a relatively long random delay between successive probe sequences if it does not receive an acknowledgement of any probe in the sequence. The noise level is reduced by minimizing transmission power. The mobile station increments the power of successive probes within each probe sequence. The first probe of each probe sequence is transmitted at a predetermined level.