The single-arm, two-stage clinical trial is a popular design utilized to evaluate oncology treatments. The designs are typically augmented with an ad hoc toxicity monitoring rule that is imposed outside of the formal two-stage design. In this work, we present a flexible bivariate single-arm clinical trial design that incorporates both response and toxicity. The design is considered flexible because it can monitor toxicity on a different schedule from the response. An example is considered in which toxicity is measured at four equally spaced times, which correspond to the data monitoring committee's meeting schedule while evaluating the response only at the second and fourth toxicity evaluations. The effect of the correlation on the types I and II error rates is examined through simulation. The simulations also examine the power over the response rates when the toxicity rate is fixed in the alternative region and vice versa. Copyright © 2012 John Wiley & Sons, Ltd.