The excess capacity of Resource Auction Multiple Access (RAMA), originally proposed for fast handoffs and resource allocations in wireless personal communications systems (PCS), is evaluated here for statistical multiplexing of speech. Using selected GSM parameters in conjunction with M-ary FSK for signaling, it is shown that, in cells with propagation delays of up to 45 mus, 216 assignments/s are feasible. Our aim is to exploit this large assignment capacity to increase channel utilization. We show that, for packet dropping probabilities of 1%, RAMA can have a multiplexing gain as high as 2.63 with fast speech detection and 2.28 with slow speech detection. RAMA permits graceful degradation during peak traffic demand by operating at higher packet dropping probabilities. We also observe that, at low values of packet dropping probability, delays experienced by transmitted packets are more evenly distributed for the case of fast speech detection while the bulk of the packets experience less delay with slow speech detection. Speech clipping statistics associated with various values of packet dropping probabilities are also presented.