let (T, <T ) be a normal, splitting λ++-tree. • For α < λ++, Tα denotes the α-th level of T, and Tλ α denotes the set of injective functions a : λ → Tα. • Tλ = α<λ++ Tα. • If a, b ∈ Tλ, we say a <T b if, for all i < λ, a(i) <T b(t). • [Tλ]2 = {(a, b) | a, b ∈ Tλ and a <T b}. • T is a λ++-super-Souslin tree if there is a function F : [Tλ]2 → λ+ such that, for all (a, b), (a, c) ∈ [Tλ]2, if F(a, b) = F(a, c), then there is i < λ such that b(i) and c(i) are ≤T -comparable.