  We consider Lorentzian wormholes supported by a phantom field and threaded by
non-trivial Yang-Mills fields, which may be regarded as hair on the Ellis
wormhole. Like the Bartnik-McKinnon solutions and their associated hairy black
holes, these hairy wormholes form infinite sequences, labeled by the node
number $k$ of their gauge field function. We discuss the throat geometry of
these wormholes, showing that odd-$k$ solutions may exhibit a double-throat,
and evaluate their global charges. We analyze the limiting behavior exhibited
by wormhole solutions as the gravitational coupling becomes large. The even-$k$
solutions approach smoothly the Bartnik-McKinnon solutions with $k/2$ nodes,
while the odd-$k$ solutions develop a singular behavior at the throat in the
limit of large coupling. In the limit of large $k$, on the other hand, an
embedded Abelian wormhole solution is approached, when the throat is large. For
smaller throats the extremal Reissner-Nordstr\"om solution plays a fundamental
role in the limit.
