Synthetic controls are used for one treated unit that lies outside its donors' range, with a pre-treatment window too short for residual-based standard errors to be trusted. We propose inference that separates the periods used to fit the synthetic control from the periods used to assess its error. Weights are fitted on an early block of pre-treatment periods, and the gap on a later block calibrates the bias and the noise. The resulting interval has finite-sample coverage under an explicit restriction on how far the counterfactual may depart from the extrapolated pre-treatment gap, for any fitting rule that uses only the early block. The leading restriction bounds the curvature of the gap and leaves its slope free, and the breakdown curvature at which the interval first includes zero states how much extrapolation a conclusion needs. We show when drift bounds calibrated from donor placebos are valid and how to allow for serial dependence. In simulations, conventional intervals undercover when the treated unit drifts from its donors, while the proposed interval covers whenever its restriction holds and the noise is serially independent. Re-analyses of three classic applications show that some well-known conclusions rest on far stronger extrapolation than others.
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