We re-examine the evolutionary dynamics of RNA secondary structures under directional selection towards an optimum RNA structure. We find that the punctuated equilibria lead to a very slow approach to the optimum, following on average an inverse power of the evolutionary time. In addition, our study of the trajectories shows that the out-of-equilibrium effects due to the evolutionary process are very weak. In particular, the distribution of genotypes is close to that arising during equilibrium stabilizing selection. As a consequence, the evolutionary dynamics leave almost no measurable out-of-equilibrium trace, only the transition genotypes (close to the border between different periods of stasis) have atypical mutational properties.