  We present theoretical and experimental studies of the decoherence of
hyperfine ground-state superpositions due to elastic Rayleigh scattering of
light off-resonant with higher lying excited states. We demonstrate that under
appropriate conditions, elastic Rayleigh scattering can be the dominant source
of decoherence, contrary to previous discussions in the literature. We show
that the elastic-scattering decoherence rate of a two-level system is given by
the square of the difference between the elastic-scattering \textit{amplitudes}
for the two levels, and that for certain detunings of the light, the amplitudes
can interfere constructively even when the elastic scattering \textit{rates}
from the two levels are equal. We confirm this prediction through calculations
and measurements of the total decoherence rate for a superposition of the
valence electron spin levels in the ground state of $^9$Be$^+$ in a 4.5 T
magnetic field.
