Dissipative Kerr solitons have paved the way to broadband and fully coherent optical frequency combs in microresonators. Here, we demonstrate numerically that slow frequency tuning of the pump laser in conjunction with phase or amplitude modulation corresponding to the free spectral range of the microresonator, provides reliable convergence of an initially excited chaotic comb state to a single dissipative Kerr soliton (DKS) state. The efficiency of this approach depends on both frequency tuning speed and modulation depth. The relevance of the proposed method is confirmed experimentally in a MgF2 microresonator. (C) 2016 Optical Society of America