  Cold molecular ions are promising candidates in various fields ranging from
precision spectroscopy and test of fundamental physics to ultra-cold 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 $^{25}\mathrm{Mg}^{+}$ ions and
sympathetic ground state cooling of $^{24}\mathrm{MgH}^{+}$. 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.
