The minimum-time, low-constant-thrust, same circular orbit rendezvous problem is studied using a relative motion description of the system dynamics. The resulting Optimal Control Problem in the thrust orientation angle is formulated using both the Direct and Indirect methods. An extensive set of test cases is numerically solved with the former, while perturbation techniques applied to the later allow to obtain several approximate solutions and provide a greater insight on the underlying physics. These results show that the structure of the solutions undergoes fundamental changes depending on the value of the non-dimensional thrust parameter.