There is currently considerable interest in two-step models of crystal nucleation, which have been implicated in a number of systems including proteins, colloids and small organic molecules. Classical nucleation theory (CNT) postulates the formation of an ordered crystalline nucleus directly from dilute vapour or solution. By contrast, the new models explain how crystallisation via a more concentrated but still fluid (disordered) phase can lead to a significant enhancement of nucleation rates. In this article, we extend recent work showing that crystal deposition from vapour can also be greatly accelerated by the operation of a two-step mechanism. The process relies on a very acute, annular wedge, in which restricted amounts of liquid condense below the bulk melting point T_m. Crystals then nucleate in the liquid condensates at sufficient temperature depressions ΔT (typically ≥30 K) below T_m, followed by rapid growth of these crystals from the saturated vapour. By using a range of model substances (neopentanol, norbornane, hexamethylcyclotrisiloxane, hexachloroethane, menthol, cyclooctane and pinacol) we show that this is a viable mechanism for substances with reasonably high absolute vapour pressures (>ca. 1 mm Hg). The lack of appreciable crystal deposition with substances of significantly lower vapour pressures (<ca. 0.01 mm Hg) is most likely due to geometric restrictions impeding diffusion in our experimental set-up. The results confirm the feasibility of a mechanism for atmospheric ice nucleation that has been suggested in the literature. Furthermore, there are thermodynamic analogies with the crystallisation of biominerals via amorphous or fluid-like precursor phases and protein nucleation in surface topographical features.