We describe a design for cancer phase I clinical trials that takes into account patients heterogeneity thought to be related to treatment susceptibility. The goal is to estimate the maximum tolerated dose (MTD) given patient’s specific dichotomous covariate value. The design is Bayesian adaptive and is an extension of escalation with overdose control (EWOC). We will assess the performance of this method by comparing the following designs via extensive simulations: (1) design using a covariate; patients are accrued to the trial sequentially and the dose given to a patient depends on his/her baseline covariate value, (2) design ignoring the covariate; patients are accrued to the trial sequentially and the dose given to a patient does not depend on his/her baseline covariate value, and (3) design using separate trials; in each group, patients are accrued to the trial sequentially and EWOC is implemented in each group. These designs are compared with respect to safety of the trial and efficiency of the estimates of the MTDs via extensive simulations. We found that ignoring a significant baseline binary covariate in the model results in a substantial number of patients being overdosed. On the other hand, accounting for a nonsignificant covariate in the model has practically no effect on the safety of the trial and efficiency of the estimates of the MTDs.