One important observation from the Ice Giants Study was that the predicted and margined thicknesses of HEEET were greater than could be woven with the currently established loom capabilities. Since the cost of a loom upgrade could be substantial and time consuming, the present work explored the entry trajectory space to determine what combinations of entry parameters would result in HEEET thicknesses that fit within the existing loom infrastructure. Toward this end, the entry trajectory space, parameterized by ballistic coefficient and entry flight path angle, was systematically explored for 45° sphere-cone geometries of 3 different radii – 0.2 m, 0.3 m, and 0.4 m – which covered the range from Galileo-derived probes considered in the Ice Giants Study, and a follow-on study on the possibility of using a single probe architecture (in terms of size and mass) for various destinations, including Venus, Saturn, Uranus, and Neptune. The entry velocities, latitudes, and azimuths at Uranus and Neptune used in the present work were taken from the Ice Giants Study. For each 3DOF trajectory generated by a NASA Ames in-house code, TRAJ, the material response and thickness were computed using another NASA Ames code, FIAT, along with a margins policy proposed by the HEEET project. In the present work, ballistic coefficients ranging from 200 kg/sq m to 350 kg/sq m were considered along with entry flight path angles ranging from -16° to -36° (primarily to allow deceleration loads to vary between 50 g and 200 g).