A series of free-electron laser (FEL) amplifier experiments were conducted at the Los Alamos National Laboratory to measure the energy extraction and the optical gain of "tapered" magnetic wigglers. A 1 ns, 1 GW CO
2laser pulse, focused at the center of a 1 m long wiggler, will interact with a coaxial, 20 MeV electron beam composed of four 30 ps wide micropulses. Although a single-pass gain of 2 percent is expected, the large difference in pump and electron pulsewidths, plus the inability to fully temporally resolve the 30 ps gain pulses, present special measurement challenges. Therefore, much attention has been given to the enhancement of the size of the gain signal relative to the power of the CO
2laser pulse. A combination of techniques involving polarization discrimination, signal nulling, and spectral bandwidth discrimination has been determined to be effective. A description of these techniques and their utilization to measure the magnitude and phase of the complex gain

and the picosecond duration of the gain pulses will be given.