Laser fusion target designs exhibit improved performance when the fusion fuel, a deuteriumtritium (DT) mixture, is frozen into a uniform, solid shell. The formation of'such a shell requires rapid isothermal cooling of the target to cryogenic temperatures. The cooling rate must be sufficiently fast to prevent significant, gravitaqtionally driven downward flow of the DT as it passes from the gaseous through the liquid state. Because it is not possible to measure the uniformity of a solid DT layer in opaque, multishell targets, we have modeled such targets to calculate the cooling rate and, hence, the expected thickness uniformity of the DT shell. The presented results provide target designers with practical guidelines for the selection of materials and configurations, which will assist in the fabrication of high-quality cryogenic targets.