Left: mass density versus Lagrangian mass (top) and radius (bottom) at the onset of core collapse for the set of 15 M_⊙ simulations produced with MESA using a mixing-length parameter of 3 and a variety of mass-loss rate scalings during the RSG phase. Right: same as left, but now for variants of model x3p0 in which some CSM has been added. The corresponding model properties are given in Table 2.