In recent years, there has been increased interest in incorporation of backfilling into dose-escalation clinical trials, which involves concurrently assigning patients to doses that have been previously cleared for safety by the dose-escalation design. Backfilling generates additional information on safety, tolerability, and preliminary activity on a range of doses below the maximum tolerated dose (MTD), which is relevant for selection of the recommended phase II dose and dose optimization. However, in practice, backfilling may not be rigorously defined in trial protocols and implemented consistently. Furthermore, backfilling designs require careful planning to minimize the probability of treating additional patients with potentially inactive agents (and/or subtherapeutic doses). In this paper, we propose a simple and principled approach to incorporate backfilling into the Bayesian optimal interval design (BOIN). The design integrates data from the dose-escalation and backfilling components of the design and ensures that the additional patients are treated at doses where some activity has been seen. Simulation studies demonstrated that the proposed backfilling BOIN design (BF-BOIN) generates additional data for future dose optimization, maintains the accuracy of the MTD identification, and improves patient safety without prolonging the trial duration.