The idea of combining the desirable features of random access (at low utilization) and reservation access (at high utilization) motivated the proposal of a combined random/reservation multiple access (CRRMA) scheme for a global beam satellite described in [13] and a multispot beam satellite described and analyzed in this paper. A key element in the proposed CRRMA protocol is the assumption of an onboard processing capability to interrogate uplink headers, to buffer successful requests, and to create and broadcast channel assignments to enhance system performance. A scheduling algorithm is introduced to enable a proper division of packet transmissions via random access and reservation access. Numerical results indicate that the proposed CRRMA protocol indeed exhibits good delay-throughput performance over a wide range of utilization.