Cold molecular ions are promising candidates in various fields ranging from precision spectroscopy and test of fundamental physics to ultracold chemistry. Control of internal and external degrees of freedom is a prerequisite for many of these applications. Motional-ground-state cooling represents the starting point for quantum logic-assisted internal state preparation, detection, and spectroscopy protocols. Robust and fast cooling is crucial to maximize the fraction of time available for the actual experiment. We optimize the cooling rate of ground-state cooling schemes for single 25Mg+ ions and sympathetic ground-state cooling of 24MgH+. In particular, we show that robust cooling is achieved by combining pulsed Raman sideband cooling with continuous quench cooling. Furthermore, we experimentally demonstrate an efficient strategy for ground-state cooling outside the Lamb-Dicke regime. © 2015 American Physical Society.