Closed form solutions have been obtained for bubble dissolution in typical polymer melts encountered in rotational molding. The solutions are in excellent agreement with experimental data available in the literature. Using these solutions, it is shown that tinder typical rotational molding conditions the polymer melts may be almost saturated. As a result, bubble shrinkage occurs over long periods. Depending on the degree of saturation, surface tension may contribute substantially to the concentration gradient that drives bubble shrinkage. It is also shown that a pressure increase imposed on a nearly saturated polymer melt leads to a steep concentration gradient at the bubble/melt interface that can cause extremely fast bubble shrinkage. Applied to the rotational molding process, such a pressure increase can result in substantial cycle-time shortening through elimination (or reduction) of the currently used excessive heating. A further benefit may be that additional resins, which at present cannot be used because of oxidation at sustained high-temperatures, can become available to the rotational molding industry. Under the undersaturated conditions created by a pressure increase, the effect of surface tension on the rate of bubble shrinkage is negligible.