  We study the transformation of multipolar decompositions of gravitational
radiation under rotations and boosts. Rotations to the remnant black hole's
frame simplify the waveforms from the merger of generic spinning black hole
binaries. Boosts may be important to get an accurate gravitational-wave
phasing, especially for configurations leading to large recoil velocities of
the remnant. As a test of our formalism we revisit the classic problem of point
particles falling into a Schwarzschild black hole. Then we highlight by
specific examples the importance of choosing the right frame in numerical
simulations of unequal-mass, spinning binary black-hole mergers.
