We propose drug screening designs based on a Bayesian decision-theoretic approach. The discussion is motivated by screening designs for phase II studies. The proposed screening designs allow consideration of multiple treatments simultaneously. In each period, new treatments can arise and currently considered treatments can be dropped. Once a treatment is removed from the phase II screening trial, a terminal decision is made about abandoning the treatment or recommending it for a future confirmatory phase III study. The decision about dropping treatments from the active set is a sequential stopping decision. We propose a solution based on decision boundaries in the space of marginal posterior moments for the unknown parameter of interest that relates to each treatment. We present a Monte Carlo simulation algorithm to implement the proposed approach. We provide an implementation of the proposed method as an easy to use R library available for public domain download (http://www.stat.rice.edu/~rusi/ or http://odin.mdacc.tmc.edu/~pm/).