Targets designed to produce ignition on the Laser Megajoule (LMJ) are being simulated in order to set specifications for target fabrication. The LMJ experimental plans include the attempt of ignition and burn of an ICF capsule with 160 laser beams, delivering up to 1.4 MJ and 380 TW. New targets needing reduced laser energy with only a small decrease in robustness have then been designed for this purpose. Working specifically on the coupling efficiency parameter, i.e. the ratio of the energy absorbed by the capsule to the laser energy, has led to the design of a rugby-ball shaped cocktail hohlraum; with these improvements, a target based on the 240-beam A1040 capsule can be included in the 160-beam laser energy-power space. Robustness evaluations of these different targets shed light on critical points for ignition, which can trade off by tightening some specifications or by preliminary experimental and numerical tuning experiments.