Long-lived diffracted intensity oscillations have been observed experimentally during thin-film deposition in several systems at temperatures below which thermally-activated diffusion is thought operative. Several models are presented for growth on fcc(100) substrates which can account for these observations. The requirement of a four-fold hollow, rather than atop, adsorption site dramatically influences film structure. Distinct, but short-lived, oscillations are found here even for random immobile adsorption. The prescription of deposition dynamics is also fundamental. Introducing a ‘downward funneling’ propensity, very short-range ‘transient mobility’ after deposition, or ‘knockout mechanisms’ greatly enhances the quasi-steady nature of film growth. The latter is reflected in a slowly-increasing or quasi-periodic film interface width. Long-lived intensity oscillations are also produced, despite the absence of any long-range mobility.