Planar polymer targets are a fundamental component of high-energy-density (HED) laser experiments in which ion acceleration by high-intensity short-pulse lasers is being investigated. HED physics experimenters at Los Alamos National Laboratory (LANL) have pioneered the development of laser-driven proton, deuteron, and carbon ion acceleration; progressive experiments have required targets of controlled composition, thickness, and density. Here, we describe recent progress made in the production of ultrathin planar CH2 and CD2 targets of varying density for these experiments, fielded at LANL's Trident laser facility.