We consider the depletion of elements from the interstellar gas onto a population of very small dust grains. Adopting a grain model in which ~4% of the cosmic C abundance is in grains with radii <=10 Å, we find that the rate of accretion onto these grains is fast enough to account for the observed large depletions of elements like Ti, without invoking unreasonably high rates of mass transfer between interstellar phases or low grain destruction rates. If these grains are composed of arene rings, then only a limited number of metal atoms can be locked up in them. The depletion would be quenched when this limit is reached, unless there is a mechanism for transferring the metals to larger grains and refreshing the very small grain population--for example, by grain coagulation and shattering in the diffuse interstellar medium (ISM). If Fe depletes onto the very small grains, then for reasonable coagulation rates there is at least one metal atom per five C atoms in the very small grain population. Furthermore, ~60% of the cosmic Fe is associated with the carbonaceous grain population. It is unclear whether this scenario is compatible with observations. However, if there is another population of very small grains, with a large capacity for holding Fe atoms, it might be the sink for the most heavily depleted elements.