  We perform a comprehensive study of on-shell recursion relations for Born
amplitudes in spontaneously broken gauge theories and identify the minimal
shifts required to construct amplitudes with a given particle content and spin
quantum numbers. We show that two-line or three-line shifts are sufficient to
construct all amplitudes with five or more particles, apart from amplitudes
involving longitudinal vector bosons or scalars, which may require at most
five-line shifts. As an application, we revisit selection rules for multi-boson
amplitudes using on-shell recursion and little-group transformations.
