We present a phase I design that is a modification to the time-to-event continual reassessment method (TITE-CRM) by Cheung and Chappell that is useful when each dose actually denotes how long a drug is administered. Because of the lengthy duration required for subjects receiving the higher doses, we enroll each subject on the best estimate of the maximum tolerated cumulative dose (MTCD) as soon as each subject is eligible. Once each previously enrolled subject is fully evaluated, we update our estimate of the MTCD and modify currently enrolled subjects to receive the MTCD if they are currently receiving a nonoptimal dose. Thus, our method is adaptive both between subjects and within subjects. We show through simulation that our study design has excellent operating characteristics that are as good as the TITE-CRM while not exposing greater numbers of subjects to doses beyond the MTCD. Our simulations are based upon a study in bone marrow transplant patients that seeks to determine how many weeks of recombinant human keratinocyte growth factor can be administered while keeping toxicity rates below a desired threshold.