We obtain a strong direct product theorem for two-party bounded round communication complexity.Let \sucr(fC) denote the maximum success probability of an r-round communication protocol that uses at most C bits of communication in computing f(xy) when (xy) . Jain et al. \cite{JainPP12} have recently showed that if \sucr(fC)32 andT(C−(r2))rn, then \sucr(nfnT)exp(−(nr2)) .Here we prove that if \suc7r(fC)32 and T(C−(rlogr))n then\sucr(nfnT)exp(−(n)) . Up to a logr factor, our result asymptotically matches the upper bound on \suc7r(nfnT) given by the trivial solution which applies the per-copy optimal protocol independently to each coordinate.The proof relies on a compression schemethat improves the tradeoff between the number of rounds and the communication complexity over known compression schemes.