(Special) Cubic fourfolds have garnered a lot of interest lately, most notably because of the difficulty posed by determining their (ir)rationality. We provide explicit descriptions of the generic members of Hassett’s divisors $C_{30}$, $C_{38}$, and $C_{44}$ in terms of Fano models of Enriques surfaces and (deformations of) Coble surfaces, and we will use these descriptions to prove the unirationality of these Noether-Lefschetz divisors. After placing this result in the context of a Gritsenko–Hulek–Sankaran type result and time permitting, we will go on to further enumerate the 13 irreducible components of $C_8 \cap C_{44}$ and describe some of them in terms of the rich geometry of Enriques surfaces. In doing so, we describe 7 new components parametrizing cubic fourfolds with trivial Clifford invariant, which are thus rational and verify Kuznetsov’s conjecture. Another 6 components have nontrivial Clifford invariant and could provide new nontrivial examples of Kuznetsov’s conjecture.