In this paper, we point out the role of anticomonotonicity in the characterization of efficient contingent claims, and in the measure of inefficiency size of financial strategies. Two random variables are said to be anticomonotonic if they move in opposite directions. We first provide necessary and sufficient conditions for a contingent claim to be efficient in markets, which might be with frictions in a quite general framework. We then compute a measure of inefficiency size for any contingent claim. We finally give several applications of these results, studying in particular the efficiency of superreplication strategies.