Conventional dose-finding methods in oncology are mainly developed for cytotoxic agents with the aim of finding the maximum tolerated dose. In phase I clinical trials with cytostatic agents, such as targeted therapies, designs with toxicity endpoints alone may not work well. For cytostatic agents, the goal is often to find the most efficacious dose that is still tolerable, although these agents are typically less toxic than cytotoxic agents and their efficacy may not monotonically increase with the dose. To effectively differentiate doses for cytostatic agents, we develop a two-stage dose-finding procedure by first identifying the toxicity upper bound of the searching range through dose escalation and then determining the most efficacious dose through dose de-escalation while toxicity is continuously monitored. In oncology, treatment efficacy often takes a relatively long period to exhibit compared with toxicity. To accommodate such delayed response, we model the time to the efficacy event by redistributing the mass of the censored observation to the right and compute the fractional contribution of the censored data. We evaluate the operating characteristics of the new dose-finding design for cytostatic agents and demonstrate its satisfactory performance through simulation studies. Copyright © 2012 John Wiley & Sons, Ltd.