A multicompartment mathematical model is presented with the goal of studying the role of dose-dense protocols in the context of combination cancer chemotherapy. Dose-dense protocols are intended to reduce the period between courses of chemotherapy from three to two weeks or less, in order to avoid the regrowth of the tumor during the meantime and achieve maximum cell kill at the end of the treatment. Inspired by clinical trials, we carry out a randomized computational study to systematically compare a variety of protocols using two drugs of different specificity. Our results suggest that cycle specific drugs can be administered at low doses between courses of treatment to arrest the relapse of the tumor. This might be a better strategy than reducing the period between cycles. (C) 2019 Elsevier B.V. All rights reserved.