Surface steps act as confining barriers for electrons in metal-surface states. Thus, narrow terraces and small single-atom-high metal islands act as low-dimensional, electron-confining structures. In sufficiently small structures, quantum-size effects are observable even at room temperature. Scanning tunneling spectroscopy is used to image the probability amplitude distributions and discrete spectra of the confined states. Examination of the electronic structure of the steps provides evidence for electron-density smoothing and the formation of step-edge states. Estimates of the electron-confining barriers are obtained.