<p>Staggered solution algorithms are a well-known alternative to monolithic approaches for solving strongly coupled multi-field problems. A coupling between the subproblems is achieved by exchanging coupling quantities between the solvers. Implicit coupling schemes are realized by letting the solvers solve each load or time step repeatedly until convergence up to a given coupling tolerance is achieved. In fluid-structure interaction as well as a variety of other problem classes, the equations governing the individual fields are nonlinear. Accordingly, each solver performs an inner iterative solution procedure that terminates once an inner tolerance is reached. The basic idea of this work builds on the possibility to adaptively adjust these inner tolerances based on carefully designed rules while preserving the black-box nature of the solvers. The resulting coupling scheme yields significant improvements in computational efficiency compared to classical schemes where the inner solver tolerances are held fixed. This is demonstrated in several numerical examples. The idea is tested in combination with state-of-the-art convergence acceleration schemes and can be realized within any staggered solution approach by only minor modifications to the participating solvers.</p>