Abstract: Two graphs G and G', each of order n, pack if there is a bijection from V(G) onto V(G') such that for each edge xy in G, f(x)f(y) is not an edge in G'. A well known result of Sauer and Spencer shows that if G and G' together contain at most 3n/2 - 1 edges, then G and G' pack. Bollobás and Eldridge proved that if max{∆(G), ∆(G')} < n-1, then 2n-2 edges is sufficient for G and G' to pack. Recently, Żak considered whether further restricting the bound on max{∆(G), ∆(G')} would increase the number of edges needed to ensure packing. Specifically, he conjectured that if max{∆(G), ∆(G')} < n-1 and |E(G)| + |E(G')| + max{∆(G), ∆(G')} ≤ 3n-7, then G and G' pack and showed that the conjecture is true asymptotically. In this talk we will show that, up to an additive constant, Żak's conjecture is true. In order to prove this result, we prove a stronger result using list packing. This is joint work with Ervin Győri, Alexandr Kostochka, and Derrek Yager.