Making single-walled carbon nanotubes (SWNTs) soluble in water is a challenging first step to use their remarkable electronic and optical properties in a variety of applications. We report that acyclic cucurbit[n]uril molecular containers 1 and 2 selectively solubilize small-diameter and low chiral angle SWNTs. The selectivity is tunable by increasing the concentration of the molecular containers or by adjusting the ionic strength of the solution. Even at a concentration 1000 times lower than typically required for surfactants, the molecular containers render SWNTs soluble in water. Molecular mechanics simulations suggest that these C-shaped acyclic molecules complex the SWNTs such that a large portion of nanotube sidewalls are exposed to the external environment. These "naked" nanotubes fluoresce upon patching the exposed surface with sodium dodecylbenzene sulfonate.