In the case of strong (implicit) coupling, where multiple coupling iterations are performed per time step, a convergence criterion is required to indicate that a time step has converged. A variety of such criteria exists, but they all compare a quantity representative of the change in interface data between successive coupling iterations, e.g., the interface residual, to a prescribed tolerance. The choice of this tolerance value is often ad hoc and based on experience. Moreover, its relationship to the tolerances of the subproblems is unclear and often not considered, even though the accuracy of the coupled simulation is inherently linked to that of the solutions of the subproblems. This work addresses this shortcoming by discussing and investigating a newly introduced criterion that does not require the choice of a coupling tolerance, but bases the convergence of the time step on the number of subproblem iterations to reach convergence. This not only eliminates the inconvenient choice of a coupling tolerance but also allows one to better judge the accuracy with which the subproblems should be solved. The new criterion can be applied to black-box solvers under the condition that they provide information on whether they have converged and on how many subproblem iterations have been run, which is not a very restrictive assumption in practice. Although the focus of this work is on fluid-structure interaction simulations, the criterion is applicable to any type of coupling of black-box solvers under the given minor condition.