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We consider the problem of amplifying the "lossiness" of functions. We say that an oracle circuit C*: {0,1}m→{0,1}* amplifies relative lossiness from ℓ/n to L/m if for every function f:{0,1}n→{0,1}n it holds that 1 If f is injective then so is Cf. 2 If f has image size of at most 2n−ℓ, then Cf has image size at most 2m−L. The question is whether such C* exists for L/m≫ℓ/n. This problem arises naturally in the context of cryptographic "lossy functions," where the relative lossiness is the key parameter. We show that for every circuit C* that makes at most t queries to f, the relative lossiness of Cf is at most L/m≤ℓ/n+O(logt)/n. In particular, no black-box method making a polynomial t=poly(n) number of queries can amplify relative lossiness by more than an O(logn)/n additive term. We show that this is tight by giving a simple construction (cascading with some randomization) that achieves such amplification.