The few existing accounts of ordinal numbers attribute to them all or almost all of the semantic properties of superlatives. This work discusses a construction problematic for these existing theories: the ordinal superlative construction (e.g. "John climbed the third highest mountain"). Existing theories give ordinals and superlatives such similar semantics that they struggle to explain how an ordinal and a superlative could join together and form a complex modifier. As an alternative, I propose a semantics according to which ordinals are exceptive modifiers of superlatives. For example, the n-th highest mountain is the mountain that, with n - 1 exceptions, is the highest. When an ordinal does not co-occur with an overt superlative (e.g. "the second train") I posit a covert superlative adjective that represents the contextual ordering. Not only does this approach account for the ordinal superlative construction, but it lends itself to a principled explanation of differences between ordinals and superlatives with respect to plurality.