In controlled clinical trials, where minimizing treatment failures is crucial, response-adaptive designs are attractive competitors to 1:1 randomized designs for comparing the success rates ϕ1 and ϕ2 of two treatments. In these designs each new treatment assignment depends on previous outcomes through some predefined rule. Here Play-The-Winner (PW), Randomized Play-The-Winner (RPW), Drop-The-Loser, Generalized Drop-the-Loser and Doubly adaptive Biased Coin Designs are considered for new treatment assignments. As frequentist inference relies on complex sampling distributions in those designs, we investigate how Bayesian inference, based on two independent Beta prior distributions, performs from a frequentist point-of-view. Performance is assessed through coverage probabilities of interval estimation procedures, power and minimization of failure count. It is shown that Bayesian inference can be favorably compared to frequentist procedures where the latter are available. The power of response-adaptive designs is generally very close to the power of 1:1 randomized design. However, failure count savings are generally small, except for the PW and Doubly adaptive Biased Coin designs in particular ranges of the true success rates. The RPW assignment rule has the worst performance, while PW, Generalized Drop-the-Loser or Doubly adaptive Biased Coin Designs may outperform other designs depending on different particular ranges of the true success rates. Copyright © 2010 John Wiley & Sons, Ltd.