What if we only allow one degree of freedom between c2ab and c2ss but self-consistently reoptimize the remaining three parameters (i.e., cC,DFT, c2ab, and s6)? We considered two possibilities: first, imposing the condition c2ab=c2ss, like in simple double hybrids like B2PLYP, 62 B2GPPLYP, 63 PBE0-2, 64 etc. as well as the combinatorially optimized ωB97M(2). The nomenclature, 'DSD', is no longer appropriate in this case and will be replaced by κDH-XC-D3BJ in the present manuscript. The second option is to exclude same-spin correlation entirely (c2ss=0), a.k.a., the DOD forms. These are of interest because they are amenable to reduced-scaling opposite-spin MP2 techniques like Laplace transform MP2 of Häser and Almlöf, which scales as Ο(N 4 ) with system size, or the tensor hypercontraction approach of Song and Martinez, which scales as Ο(N 3 ). As expected, constraining c2ab=c2ss always increases WTMAD2 over the κDSD forms. Both for κDH-PBEPBE-D3BJ and κDH-PBEP86-D3BJ, we found the lowest WTMAD2 at κmin=2.5, corresponding to 0.11 and 0.10 kcal/mol reductions, respectively, compared to their unregularized forms. For κDH-BLYP-D3BJ, the WTMAD2 gap between κmin (κ value for which we obtain the minimum WTMAD2) and κ=∞ is ~0.08 kcal/mol. Interestingly, for the κDOD functionals, GLPT2 regularization does more harm than good, and the unregularized forms always offer the best performance (see Figure ).