This paper studies information design in multi-agent systems with binary actions and strategic complementarities, where an external designer influences agent behaviour through signals. The analysis focuses on the smallest equilibrium of the induced Bayesian game, capturing conservative, coordination-averse behaviour. We show that under convexity conditions, the robustly implementable optimum takes a simple threshold form, yielding perfect coordination at each state. This is a preprint version of a paper accepted for publication at the 25th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2026). The final version will appear in the conference proceedings.