The biased coin up-and-down design (BCD) is used to allocate doses in phase I clinical trials. The BCD requires that the treatment response or the toxicity evaluation is observed quickly. In trials with a long treatment evaluation, the BCD will lead to long trial duration because a new patient cannot be enrolled until the preceding patient has completed the evaluation period. We propose a simple method to modify the BCD that will reduce the trial duration without significantly affecting the estimate of the target dose. The idea is to allocate a dose to each patient as he or she arrives based on the toxicity information of the last completed subject. This allows multiple patients to be concurrently under evaluation. A simulation study shows that this modification does not adversely affect the precision of the recommended dose, as estimated by isotonic regression, but it does significantly reduce the total time to complete the study.