The performance of triple-picket deuterium-tritium cryogenic target designs on the OMEGA Laser System [T. R. Boehly, Opt. Commun. 133, 495 (1997)] is reported. These designs facilitate control of shock heating in low-adiabat inertial confinement fusion targets. Areal densities up to 300 mg/cm2 (the highest ever measured in cryogenic deuterium-tritium implosions) are inferred in the experiments with an implosion velocity approximately 3x10(7) cm/s driven at peak laser intensities of 8x10(14) W/cm2. Extension of these designs to ignition on the National Ignition Facility [J. A. Paisner, Laser Focus World 30, 75 (1994)] is presented.