In this talk we will present a near-optimal compression scheme for bounded-round randomized 2-party communication protocols. Previously, such a scheme was only known for protocols where the inputs to the parties are independent. The results yield a new optimal direct sum theorem for bounded-round communication. They also reveal a tight connection between the Information Cost of a problem and its amortized Communication Complexity. Joint work with Anup Rao. A talk by Anup on the prequel to this work can be found here: http://www.cs.washington.edu/education/courses/590z/10wi/media/10wi01.mov This talk will be independent of Anup's talk.