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Merging firms regularly argue that mergers involving capacity-constrained firms are unlikely to be anticompetitive, because the incentive for the merged firm to raise prices and reduce quantity may not be strong enough to generate slack in the capacity constraints and lead to higher prices. We construct a modified notion of upward pricing pressure called ccGUPPI, or capacity constrained GUPPI, which accounts for the upward prices pressure from binding capacity constraints, in addition to standard merger price effects. ccGUPPI is sufficient to correctly predict whether a merger of capacity-constrained firms will have positive price effects, irrespective of the functional form of demand. Further, using Monte Carlo simulation, we show that ccGUPPI is generally a useful proxy for actual price effects, with lower informational requirements than full merger simulation.