The small-signal regime of the free-electron laser is analyzed for single-frequency, uniform-wiggler operation, taking diffraction into account. Exponentially growing modes are found with profiles independent of the longitudinal coordinate. Maximum gain occurs for a positive value of the energy detuning, though the gain on resonance is nearly maximal. If the current transverse distribution is uniform and sharp-edged, analytic solutions are obtained in terms of Bessel and Hankel functions with complex arguments. Positive energy detuning broadens the laser modes, while negative detuning concentrates them within the electron beam.