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Existing serving systems execute these branches eagerly or under fixed caps. We show that both are brittle: eager admission inflates the shared decode step, degrading co-batched requests in serial stages, while conservative fixed caps forgo the throughput that motivated exposing branches in the first place. We call the excess step latency caused by admitted branches the branch externality and show that the safe width depends on batch composition, context lengths, and accumulated slack, all of which change continuously over a workload trace. We introduce TAPER, a per-step admission controller that treats extra branches as opportunistic work, admitted only when the predicted branch externality fits within the batch's current slack budget. 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