Here, we present a method based on rigid body mechanics and the use of virtual sites to optimize the behavior of highly constrained topologies such as the Martini 2 cholesterol topology in terms of LINCS convergence without affecting the original parametrization of the molecule. First, we recapitulate the fundamental problem with the joint use of coupled constraints and the LINCS algorithm. We provide a set of guidelines that can help to avoid the creation of such constraints, and we present a script that enables the detection of constraintrelated issues without explicitly performing any simulation. We apply the script to assess the behavior of constrained molecules in the Martini 3 small molecule library and different atomistic cholesterol topologies. Second, we modify the cholesterol constraint topology to reduce the time-step dependence and the temperature gradients of the system. Finally, we perform Martini 2 simulations of (i) a single cholesterol molecule, (ii) a phase separating lipid bilayer, and (iii) a G-protein coupled receptor (GPCR) embedded in a cholesterol containing membrane using both the original Martini 2 and our optimized cholesterol models to demonstrate the improvements introduced by our model.