The Ringbom or hybrid Stirling engine, essentially dormant for some 70 years, is experiencing a vigorous rebirth following recent fundamental discoveries concerning its unique mode of operation. In this paper the author’s earlier mathematical model of Ringbom engine operation is extended to include volume variation effects due to the displacer rod. This injects a new parameter, the rod-to-displacer area ratio, into the theory improving its fidelity and increasing its predictive power. It is rigorously shown that the main theorem characterizing overdriven mode operation, the basic regime of stable running for hybrids, remains valid in the extended model and is presented here in a new form.