The character of the surface state wave function on regularly stepped Cu(111) is reinvestigated. It is shown that the qualitative change at terrace lengths around 17 A observed previously by Ortega et al. [Phys. Rev. Lett. 84, 6110 (2000)]] must necessarily be described as a change from a propagating superlattice state to a terrace-confined quasi-one-dimensional state. This reconciles previous, apparently contradictory experimental results and sheds new light on the behavior of nearly free electrons in nanostructures. Possible mechanisms driving the localization are discussed on the basis of the surface state bulk penetration depth, which has been measured in both regimes.