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An upper bound on the capacity of a primitive three-node discrete memoryless relay channel is considered, where a source X wants to send information to destination Y with the help of a relay Z. The signals at each node are also denoted as X, Y, and Z, respectively, with a slight abuse of notation. Y and Z are independent given X, and the link from Z to Y is lossless with rate R ₀ . A new inequality is introduced to upper-bound the capacity when the encoding rate is beyond the capacities of both individual links XY and XZ. It is based on generalizing the blowing-up lemma, linking conditional entropy to decoding error, and generalizing channel simulation to the case with side information. The upper bound is strictly better than the well-known cut-set bound in several cases when the latter is C _XY +R ₀ , with C _XY being the channel capacity between X and Y. One particular case is when the channel is stochastically …