  We provide a uniform upper bound on the minimal drift so that the
one-per-site frog model on a $d$-ary tree is recurrent. To do this, we
introduce a subprocess that couples across trees with different degrees.
Finding couplings for frog models on nested sequences of graphs is known to be
difficult. The upper bound comes from combining the coupling with a new,
simpler proof that the frog model on a binary tree is recurrent when the drift
is sufficiently strong. Additionally, we describe a coupling between frog
models on trees for which the degree of the smaller tree divides that of the
larger one. This implies that the critical drift has a limit as $d$ tends to
infinity along certain subsequences.
