The aim of phase I combination dose-finding studies in oncology is to estimate one or several maximum tolerated doses (MTDs) from a set of available dose levels of two or more agents. Combining several agents can indeed increase the overall anti-tumor action but at the same time also increase the toxicity. It is, however, unreasonable to assume the same dose-toxicity relationship for the combination as for the simple addition of each single agent because of a potential antagonist or synergistic effect. Therefore, using single-agent dose-finding methods for combination therapies is not appropriate. In recent years, several authors have proposed novel dose-finding designs for combination studies, which use either algorithm-based or model-based methods. The aim of our work was to compare, via a simulation study, six dose-finding methods for combinations proposed in recent years. We chose eight scenarios that differ in terms of the number and location of the true MTD(s) in the combination space. We then compared the performance of each design in terms of correct combination selection, patient allocation, and mean number of observed toxicities during the trials. Our results showed that the model-based methods performed better than the algorithm-based ones. However, none of the compared model-based designs gave consistently better results than the others.