  The vibrational branching ratios of SrOH for radiative decay to the ground
electronic state, $X^{2}\Sigma^{+}$, from the first two electronically excited
states, $A^{2}\Pi$ and $B^{2}\Sigma^{+}$, are determined experimentally at the
$\sim10^{-5}$ level. The observed small branching ratios enable the design of a
full, practical laser-cooling scheme, including magneto-optical trapping and
sub-Doppler laser cooling, with $>10^4$ photon scatters per molecule. Ab initio
calculations sensitive to weak vibronic transitions are performed to facilitate
the experimental measurement and analysis, and show good agreement with
experiment.
