  We analyze different microscopic RNA models at zero temperature. We discuss
both the most simple model, that suffers a large degeneracy of the ground
state, and models in which the degeneracy has been remove, in a more or less
severe manner. We calculate low-energy density of states using a coupling
perturbing method, where the ground state of a modified Hamiltonian, that
repels the original ground state, is determined. We evaluate scaling exponents
starting from measurements of overlaps and energy differences. In the case of
models without accidental degeneracy of the ground state we are able to clearly
establish the existence of a glassy phase with $\theta \simeq 1/3$.
