The goal of phase I cancer trials is to determine the highest dose of a treatment regimen with an acceptable toxicity rate. Traditional designs for phase I trials, such as the Continual Reassessment Method (CRM) and the 3 + 3 design, require each patient or a cohort of patients to be fully evaluated for the dose-limiting toxicity (DLT) before new patients can be enrolled. As such, the trial duration may be prohibitively long. The Time-to-Event Continual Reassessment Method (TITE-CRM, Cheung and Chappell, 2000) circumvents this limitation by allowing staggered patient accrual without the need for complete DLT follow-up of previously treated patients. However, in the setting of fast patient accrual and late-onset toxicities, the TITE-CRM results in overly aggressive dose escalation and exposes a considerable number of patients to toxic doses. We examine a modification to the TITE-CRM proposed by the original TITE-CRM creator and propose an alternative approach useful in this setting by incorporating an accrual suspension rule. A simulation study designed based on a neuro-oncology trial indicates that the modified methods provide a much improved degree of safety than the TITE-CRM while maintaining desirable design accuracy. The practical aspects of the proposed designs are discussed. The modifications presented are useful when planning phase I trials involving chemoradiation therapy.