The involvement of robots in warehouse automation poses new problems to research in logistic tasks such as tight packaging, in which a container must be completely filled with items, in a regular and ordered manner, leaving minimum clearance between them. This work investigates the effect of a reliable placing strategy using a system with passive compliance to improve robustness and success rate in such a task. The methodology is integrated into a full pipeline to execute the packaging operation and is evaluated in a real robot, using a mechanically compliant hybrid gripper with variable stiffness, exploring the roles of the hand configuration and stiffness level in the task execution. Along different evaluation tasks, the results show an improvement in success rate thanks to a reliable insertion strategy, when compared to a trivial one. They also demonstrate the efficacy of using variable stiffness to reduce error propagation.