Large-scale motions in wall-bounded turbulent flows are frequently interpreted as resulting from an aggregation process of smaller-scale structures. Here, we explore the alternative possibility that such large-scale motions are themselves self-sustained and do not draw their energy from smaller-scale turbulent motions activated in buffer layers. To this end, it is first shown that large-scale motions in turbulent Couette flow at Re = 2150 self-sustain, even when active processes at smaller scales are artificially quenched by increasing the Smagorinsky constant C s in large-eddy simulations (LES). These results are in agreement with earlier results on pressure-driven turbulent channel flows. We further investigate the nature of the large-scale coherent motions by computing upper-and lower-branch nonlinear steady solutions of the filtered (LES) equations with a Newton-Krylov solver, and find that they are connected by a saddle-node bifurcation at large values of C s. Upper-branch solutions for the filtered large-scale motions are computed for Reynolds numbers up to Re = 2187 using specific paths in the Re-C s parameter plane and compared to large-scale coherent motions. Continuation to C s = 0 reveals that these large-scale steady solutions of the filtered equations are connected to the Nagata-Clever-Busse-Waleffe branch of steady solutions of the Navier-Stokes equations. In contrast, we find it impossible to connect the latter to buffer-layer motions through a continuation to higher Reynolds numbers in minimal flow units.