The design of soft robots' deformable bodies is complex, partly due to the trade-off between softness for motion and stiffness for force generation. Self-contacts in soft structures can be used to address this problem but have been marginally investigated. In parallel, parametric designs and computational optimization tools constitute an important trend paving the way toward shareable and reproducible results. In this paper, we study the potential of self-contacts in the design of soft grippers using a multi-objective design optimization environment. This open-source environment is targeted toward grasping tasks and is used both for design and model calibration. Soft fingers with improved grasping quality and energy are obtained, taking into account different friction coefficients at the contacts and different shapes of the objects to grasp. They are experimen-tally validated in terms of mechanical behavior and grasping performances.