We consider ultimatum bargaining over the provision of a public good. Offer-maker and responder can delegate their decisions to agents whose actual decision rules are opaque. We show that the responder will benefit from strategic opacity, even with bilateral delegation. The incomplete information created by strategic opacity choices does not lead to inefficient negotiation failure in equilibrium. Inefficiencies arise from an inefficient provision level. While an agreement will always be reached, the public good provision will fall short of the socially desirable level. Compared with unilateral delegation, bilateral delegation is never worse from a welfare perspective.