The fast ignition (FI) concept requires the generation of a compact, dense, pure fuel mass accessible to an external ignition source. The current baseline FI target is a shell fitted with a re-entrant cone extending to near its center. Conventional direct or indirect drive collapses the shell near the tip of the cone and then an ultra-intense laser pulse focused to the inside cone tip generates high-energy electrons to ignite the dense fuel. Theoretical investigations of this concept with a modest 2-D calculational scheme have sparsely explored the large design space and the tradeoffs available to optimize compaction of the fuel and maintain the integrity of the cone. Experiments have generally validated the modeling while revealing additional complexities. Away from the cone, the shell collapses much as does a conventional implosion, generating a hot, low-density inner core plasma which exhausts out toward the tip of the cone. The hot, low-density inner core can impede the compaction of the cold fuel, lowering the implosion/burn efficiency and the gain, and jetting toward the cone tip can affect the cone integrity. Thicker initial fuel layers, lower velocity implosions, and drive asymmetries can lead to decreased efficiency in converting implosion kinetic energy into compression.more » Ignition and burn hydrodynamic studies have revealed strategies for generating additional convergence and compression in the FI context. We describe 2-D and 1-D approaches to optimizing designs for cone-guided fast-ignition.« less