<span style="white-space: normal;">I derive novel upper bounds on the revenue loss from mechanism simplicity in two related economic selling problems. First, in the Bulow and Roberts (1989) capacity-constrained selling problem, I derive a tight upper bound on the revenue ratio between the optimal mechanism and the best posted-price mechanism. This bound has value 2-c, where c is the seller's capacity. Second, I extend this result to give an upper bound on the revenue ratio between the optimal auction and the best posted-price mechanism in the (symmetric, potentially irregular) Myersonian multi-item auction. This bound is tight in the large auction limit, where it has limiting value 2-m/n, for an m-item, n-bidder auction. My derivations make novel use of a concavification procedure; the technique appears portable to other approximation questions in economic theory.</span>