  We classify the irreducible unitary representations of closed simple groups
of automorphisms of trees acting $2$-transitively on the boundary and whose
local action at every vertex contains the alternating group. As an application,
we confirm Claudio Nebbia's CCR conjecture on trees for
$(d_0,d_1)$-semi-regular trees such that $d_0,d_1\in \Theta$, where $\Theta$ is
an asymptotically dense set of positive integers.
