Target designs that utilize heavy-ion beams with two substantially different particle energies are presented. Low-energy ions of moderate power are used to directly drive a spherical-shell target that is cryogenically layered with a deuterium-tritium (DT) mixture. The purpose of this first pulse is to compress the DT fuel and tamper; compressions of a hundred to a few hundred times solid density appear possible. Following compression the target is irradiated with a high-particle energy and high-power pulse. The main purpose of the second pulse is to bring the central DT region to ignition. Additional compression of no more than 10 is needed. For targets with a low-Z pusher, gains greater than a hundred are possible with an ignition pulse of 1000 TW and a heavy-ion particle energy of 40 GeV. Pulse requirements, finite focusing effects, and symmetry requirements are discussed.