We measure directed flow (v_{1}) for charged particles in Au+Au and Cu+Cu collisions at sqrt[s_{NN}]=200 and 62.4 GeV, as a function of pseudorapidity (eta), transverse momentum (p_{t}), and collision centrality, based on data from the STAR experiment. We find that the directed flow depends on the incident energy but, contrary to all available model implementations, not on the size of the colliding system at a given centrality. We extend the validity of the limiting fragmentation concept to v_{1} in different collision systems, and investigate possible explanations for the observed sign change in v_{1}(p_{t}).