Direct-drive target designs below self-ignition threshold are proposed for the laser megajoule in the context of shock-ignition. Two distinct initial aspect ratios are considered and laser pulses are shaped following a classical Kidder's law in order to achieve an implosion velocity of 300 km/s, an in-fight adiabat close to unity and to maximize the peak areal density. The pulse shapes are adjusted to arrange shock timing at the inner side of the DT fuel. The robustness of the laser pulse is addressed by the means of random variations around the initial Kidder's laws. Correlation matrices show no significant correlations between laser parameters. An admissible envelope of laser pulse is given for both designs in order to warrant more than 80% of the best peak areal density. Variations of laser drive power produce variations of implosion velocities in the range 250–370 km/s. Self-ignition threshold is achieved and thermonuclear energy are produced in the range 3 kJ–27 MJ. Finally, the random procedure shows that it is possible to improve the first deterministic optimization and the laser pulses are given.