We study dynamic bargaining with asymmetric information and interdependent values. We base our analysis on the equilibria characterized by Deneckere and Liang (2006) for the gap case. We show that as the gap between the cost and value of the weakest type shrinks to zero, the continuous time limit of equilibria changes dramatically from rare bursts of trade with long periods of inactivity to smooth screening over time. In the double limit prices are independent of the shape of the distribution of values. When the uninformed agent's ability to commit to prices disappears so do her rents, yet trade still exhibits delay.