  We apply the techniques of our previous paper to study joint eigenfunctions
of the Laplacian and one Hecke operator on compact congruence surfaces, and
joint eigenfunctions of the two partial Laplacians on compact quotients of
$\mathbb{H}\times\mathbb{H}$. In both cases, we show that quantum limit
measures of such sequences of eigenfunctions carry positive entropy on almost
every ergodic component. Together with prior work of the second named author,
this implies Quantum Unique Ergodicity for such functions.
