We consider the problem of estimating the jump tails of an Ito semimartingale. The new estimation strategy developed in the paper is based on in-fill asymptotic arguments and a method-of-moments type procedure that explicitly utilizes the weak assumption of regular variation in the jump tails. On implementing the new procedures with actual high-frequency data for the aggregate market portfolio, we find strong evidence for richer and much more complex dynamic dependencies in the jump tails than hitherto considered in the literature.