[en] A number of physics issues are relevant to the design of a high extraction efficiency wiggler for a free-electron laser (FEL) oscillator. The physics issues the authors' address here are the following: (1) the balance of small-signal gain with maximum extraction efficiency when the wiggler length is constrained; (2) degradation of the electron extraction efficiency with the onset of the sideband instability and the use of corrective frequency filtering techniques to suppress the sideband; (3) reduction of efficiency due to the structure of the electron micropulse and that due to cavity length detuning; and (4) 3-D effects such as electron-beam emittance, focusing and refractive effects, misalignments, and the self-consistent FEL resonator solution with the electron beam present. The authors have developed several numerical models with increasing complexity to isolate and address the above physics issues