Determining the maximum tolerated dose (MTD) is the main challenge of phase I clinical trials. There are many methods in the literature to determine the MTD. The D-optimal design can also be used to find the MTD. The D-optimal design depends on the Fisher information matrix (FIM), and it minimizes the generalized variance of the parameter estimates. However, the D-optimal design is yet to receive much attention from clinicians. Since a dose-response model is usually non-linear, the FIM depends on the unknown model parameters. To optimize the FIM through the D-criterion, values need to be assumed for the model parameters. This paper focuses on investigating four different D-optimal designs depending on parameter values: design based on posterior Bayes estimators, design based on maximum likelihood estimators, sequential Bayesian design and two-stage Bayesian design. Six plausible dose-response scenarios and a real scenario are investigated through a simulation study. Except for the D-optimal design that utilizes maximum likelihood estimates in FIM optimization, all other D-optimal designs are found very competitive for the correct MTD recommendation. The D-optimal designs are also compared with an A-optimal design. The performance of A-optimal design is not attractive as these designs. Because of its numerical simplicity compared to the others, the posterior-based D-optimal design is recommended for dose-finding in phase I clinical trials.