Inertial confinement fusion requires very smooth and uniform solid deuterium-tritium (D-T) fuel layers. The National Ignition Facility (NIF) point design calls for a 65- to 75-m-thick D-T fuel layer inside of a 2-mm-diam spherical ablator shell to be 1.5 K below the D-T melting temperature (Tm) of 19.79 K. We find that the layer quality depends on the initial crystal seeding, with the best layers grown from a single seed. The low modes of the layer are controlled by thermal shimming of the hohlraum and meet the NIF requirement with beryllium shells and nearly meet the requirement with plastic shells. The remaining roughness is localized in grain-boundary grooves and is minimal for a single crystal layer. Once formed, the layers need to be cooled to Tm - 1.5 K. We have studied dependence of the roughness on the cooling rate and found that cooling at rates of 0.03 to 0.5 K/s is able to preserve the layer structure for a few seconds after reaching the desired temperature. The entire fuel layer remains in contact with the shell during this rapid cooling. Thus, rapid cooling of the layers is able to satisfy the NIF ignition requirements.