Different target designs are discussed which may be used in an inertial confinement fusion (ICF) reactor system driven by lithium ions. These different designs are for various energies of the incident ions. For ion energies of the order of 30 MeV, targets without a tamper can be used; however, for higher energies, tamped targets are needed. The paper presents simulation results for the compression, ignition and burn of the latter type of target. These are single-shell multi-layered targets containing 3.2 mg of D-T fuel. The gain of these targets is sufficiently high that they can be used in an ICF reactor system.