The success of direct-drive-ignition target designs depends on two issues: the ability to maintain the main fuel adiabat at a low level and the control of the nonuniformity growth during the implosion. A series of experiments was performed on the OMEGA Laser System ͓T. R. Boehly, D. L. Brown, R. S. Craxton et al., Opt. Commun. 133, 495 ͑1997͔͒ to study the physics of low-adiabat, high-compression cryogenic fuel assembly. Modeling these experiments requires an accurate account for all sources of shell heating, including shock heating and suprathermal electron preheat. To increase calculation accuracy, a nonlocal heat-transport model was implemented in the 1D hydrocode. High-areal-density cryogenic fuel assembly with R Ͼ 200 mg/ cm 2 ͓T. C. Sangster, V. N. Goncharov, P. B. Radha et al., "High-areal-density fuel assembly in direct-drive cryogenic implosions," Phys. Rev. Lett. ͑submitted͔͒ has been achieved on OMEGA in designs where the shock timing was optimized using the nonlocal treatment of the heat conduction and the suprathermal-electron preheat generated by the two-plasmon-decay instability was mitigated.